Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(16,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.3 | ||
Root | \(-0.733051 - 1.26968i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.16 |
Dual form | 39.4.e.c.22.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.733051 | + | 1.26968i | 0.259173 | + | 0.448900i | 0.966021 | − | 0.258465i | \(-0.0832168\pi\) |
−0.706848 | + | 0.707366i | \(0.749883\pi\) | |||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | 2.92527 | − | 5.06672i | 0.365659 | − | 0.633340i | ||||
\(5\) | 9.85055 | 0.881060 | 0.440530 | − | 0.897738i | \(-0.354791\pi\) | ||||
0.440530 | + | 0.897738i | \(0.354791\pi\) | |||||||
\(6\) | −2.19915 | + | 3.80904i | −0.149633 | + | 0.259173i | ||||
\(7\) | −14.9698 | + | 25.9285i | −0.808293 | + | 1.40001i | 0.105752 | + | 0.994393i | \(0.466275\pi\) |
−0.914045 | + | 0.405613i | \(0.867058\pi\) | |||||||
\(8\) | 20.3063 | 0.897421 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 7.22095 | + | 12.5071i | 0.228347 | + | 0.395508i | ||||
\(11\) | −23.4629 | − | 40.6389i | −0.643120 | − | 1.11392i | −0.984732 | − | 0.174076i | \(-0.944306\pi\) |
0.341612 | − | 0.939841i | \(-0.389027\pi\) | |||||||
\(12\) | 17.5516 | 0.422227 | ||||||||
\(13\) | 3.71050 | − | 46.7251i | 0.0791621 | − | 0.996862i | ||||
\(14\) | −43.8945 | −0.837950 | ||||||||
\(15\) | 14.7758 | + | 25.5925i | 0.254340 | + | 0.440530i | ||||
\(16\) | −8.51663 | − | 14.7512i | −0.133072 | − | 0.230488i | ||||
\(17\) | 24.1308 | − | 41.7958i | 0.344270 | − | 0.596292i | −0.640951 | − | 0.767582i | \(-0.721460\pi\) |
0.985221 | + | 0.171289i | \(0.0547932\pi\) | |||||||
\(18\) | −13.1949 | −0.172782 | ||||||||
\(19\) | −60.1501 | + | 104.183i | −0.726283 | + | 1.25796i | 0.232161 | + | 0.972677i | \(0.425421\pi\) |
−0.958444 | + | 0.285282i | \(0.907913\pi\) | |||||||
\(20\) | 28.8155 | − | 49.9100i | 0.322167 | − | 0.558010i | ||||
\(21\) | −89.8188 | −0.933337 | ||||||||
\(22\) | 34.3990 | − | 59.5807i | 0.333358 | − | 0.577393i | ||||
\(23\) | −65.3485 | − | 113.187i | −0.592440 | − | 1.02614i | −0.993903 | − | 0.110260i | \(-0.964832\pi\) |
0.401463 | − | 0.915875i | \(-0.368502\pi\) | |||||||
\(24\) | 30.4595 | + | 52.7573i | 0.259063 | + | 0.448710i | ||||
\(25\) | −27.9667 | −0.223734 | ||||||||
\(26\) | 62.0459 | − | 29.5407i | 0.468008 | − | 0.222823i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 87.5815 | + | 151.696i | 0.591120 | + | 1.02385i | ||||
\(29\) | 97.4729 | + | 168.828i | 0.624147 | + | 1.08105i | 0.988705 | + | 0.149874i | \(0.0478867\pi\) |
−0.364558 | + | 0.931181i | \(0.618780\pi\) | |||||||
\(30\) | −21.6629 | + | 37.5212i | −0.131836 | + | 0.228347i | ||||
\(31\) | −32.0123 | −0.185470 | −0.0927351 | − | 0.995691i | \(-0.529561\pi\) | ||||
−0.0927351 | + | 0.995691i | \(0.529561\pi\) | |||||||
\(32\) | 93.7115 | − | 162.313i | 0.517688 | − | 0.896661i | ||||
\(33\) | 70.3886 | − | 121.917i | 0.371306 | − | 0.643120i | ||||
\(34\) | 70.7565 | 0.356901 | ||||||||
\(35\) | −147.461 | + | 255.409i | −0.712155 | + | 1.23349i | ||||
\(36\) | 26.3275 | + | 45.6005i | 0.121886 | + | 0.211113i | ||||
\(37\) | 16.2125 | + | 28.0808i | 0.0720355 | + | 0.124769i | 0.899793 | − | 0.436316i | \(-0.143717\pi\) |
−0.827758 | + | 0.561086i | \(0.810384\pi\) | |||||||
\(38\) | −176.372 | −0.752931 | ||||||||
\(39\) | 126.961 | − | 60.4474i | 0.521283 | − | 0.248188i | ||||
\(40\) | 200.028 | 0.790681 | ||||||||
\(41\) | 120.913 | + | 209.427i | 0.460570 | + | 0.797731i | 0.998989 | − | 0.0449461i | \(-0.0143116\pi\) |
−0.538419 | + | 0.842677i | \(0.680978\pi\) | |||||||
\(42\) | −65.8418 | − | 114.041i | −0.241895 | − | 0.418975i | ||||
\(43\) | −48.2044 | + | 83.4924i | −0.170956 | + | 0.296104i | −0.938754 | − | 0.344587i | \(-0.888019\pi\) |
0.767799 | + | 0.640691i | \(0.221352\pi\) | |||||||
\(44\) | −274.541 | −0.940651 | ||||||||
\(45\) | −44.3275 | + | 76.7774i | −0.146843 | + | 0.254340i | ||||
\(46\) | 95.8076 | − | 165.944i | 0.307088 | − | 0.531892i | ||||
\(47\) | 539.015 | 1.67284 | 0.836419 | − | 0.548090i | \(-0.184645\pi\) | ||||
0.836419 | + | 0.548090i | \(0.184645\pi\) | |||||||
\(48\) | 25.5499 | − | 44.2537i | 0.0768293 | − | 0.133072i | ||||
\(49\) | −276.690 | − | 479.241i | −0.806676 | − | 1.39720i | ||||
\(50\) | −20.5010 | − | 35.5088i | −0.0579857 | − | 0.100434i | ||||
\(51\) | 144.785 | 0.397528 | ||||||||
\(52\) | −225.889 | − | 155.484i | −0.602406 | − | 0.414648i | ||||
\(53\) | −152.277 | −0.394657 | −0.197328 | − | 0.980337i | \(-0.563226\pi\) | ||||
−0.197328 | + | 0.980337i | \(0.563226\pi\) | |||||||
\(54\) | −19.7924 | − | 34.2814i | −0.0498778 | − | 0.0863909i | ||||
\(55\) | −231.122 | − | 400.315i | −0.566627 | − | 0.981427i | ||||
\(56\) | −303.981 | + | 526.511i | −0.725379 | + | 1.25639i | ||||
\(57\) | −360.901 | −0.838640 | ||||||||
\(58\) | −142.905 | + | 247.519i | −0.323524 | + | 0.560359i | ||||
\(59\) | −163.896 | + | 283.876i | −0.361652 | + | 0.626399i | −0.988233 | − | 0.152957i | \(-0.951120\pi\) |
0.626581 | + | 0.779356i | \(0.284454\pi\) | |||||||
\(60\) | 172.893 | 0.372007 | ||||||||
\(61\) | 49.2090 | − | 85.2325i | 0.103288 | − | 0.178900i | −0.809749 | − | 0.586776i | \(-0.800397\pi\) |
0.913037 | + | 0.407876i | \(0.133730\pi\) | |||||||
\(62\) | −23.4666 | − | 40.6454i | −0.0480688 | − | 0.0832576i | ||||
\(63\) | −134.728 | − | 233.356i | −0.269431 | − | 0.466668i | ||||
\(64\) | 138.515 | 0.270537 | ||||||||
\(65\) | 36.5504 | − | 460.267i | 0.0697465 | − | 0.878295i | ||||
\(66\) | 206.394 | 0.384929 | ||||||||
\(67\) | 220.575 | + | 382.048i | 0.402202 | + | 0.696635i | 0.993991 | − | 0.109458i | \(-0.0349115\pi\) |
−0.591789 | + | 0.806093i | \(0.701578\pi\) | |||||||
\(68\) | −141.178 | − | 244.528i | −0.251771 | − | 0.436080i | ||||
\(69\) | 196.046 | − | 339.561i | 0.342045 | − | 0.592440i | ||||
\(70\) | −432.385 | −0.738284 | ||||||||
\(71\) | −172.524 | + | 298.821i | −0.288379 | + | 0.499486i | −0.973423 | − | 0.229015i | \(-0.926449\pi\) |
0.685044 | + | 0.728501i | \(0.259783\pi\) | |||||||
\(72\) | −91.3784 | + | 158.272i | −0.149570 | + | 0.259063i | ||||
\(73\) | 773.839 | 1.24070 | 0.620349 | − | 0.784326i | \(-0.286991\pi\) | ||||
0.620349 | + | 0.784326i | \(0.286991\pi\) | |||||||
\(74\) | −23.7691 | + | 41.1694i | −0.0373393 | + | 0.0646735i | ||||
\(75\) | −41.9501 | − | 72.6597i | −0.0645864 | − | 0.111867i | ||||
\(76\) | 351.911 | + | 609.528i | 0.531144 | + | 0.919969i | ||||
\(77\) | 1404.94 | 2.07932 | ||||||||
\(78\) | 169.818 | + | 116.889i | 0.246514 | + | 0.169680i | ||||
\(79\) | −150.332 | −0.214097 | −0.107049 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107049 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(80\) | −83.8934 | − | 145.308i | −0.117245 | − | 0.203074i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −177.270 | + | 307.041i | −0.238734 | + | 0.413500i | ||||
\(83\) | 337.966 | 0.446947 | 0.223473 | − | 0.974710i | \(-0.428260\pi\) | ||||
0.223473 | + | 0.974710i | \(0.428260\pi\) | |||||||
\(84\) | −262.745 | + | 455.087i | −0.341283 | + | 0.591120i | ||||
\(85\) | 237.702 | − | 411.711i | 0.303322 | − | 0.525369i | ||||
\(86\) | −141.345 | −0.177228 | ||||||||
\(87\) | −292.419 | + | 506.484i | −0.360351 | + | 0.624147i | ||||
\(88\) | −476.444 | − | 825.226i | −0.577149 | − | 0.999652i | ||||
\(89\) | −84.9567 | − | 147.149i | −0.101184 | − | 0.175256i | 0.810989 | − | 0.585062i | \(-0.198930\pi\) |
−0.912173 | + | 0.409806i | \(0.865596\pi\) | |||||||
\(90\) | −129.977 | −0.152231 | ||||||||
\(91\) | 1155.96 | + | 795.673i | 1.33163 | + | 0.916584i | ||||
\(92\) | −764.649 | −0.866524 | ||||||||
\(93\) | −48.0184 | − | 83.1703i | −0.0535406 | − | 0.0927351i | ||||
\(94\) | 395.125 | + | 684.377i | 0.433554 | + | 0.750937i | ||||
\(95\) | −592.511 | + | 1026.26i | −0.639899 | + | 1.10834i | ||||
\(96\) | 562.269 | 0.597774 | ||||||||
\(97\) | −107.101 | + | 185.504i | −0.112107 | + | 0.194176i | −0.916620 | − | 0.399760i | \(-0.869093\pi\) |
0.804512 | + | 0.593936i | \(0.202427\pi\) | |||||||
\(98\) | 405.656 | − | 702.616i | 0.418137 | − | 0.724234i | ||||
\(99\) | 422.332 | 0.428747 | ||||||||
\(100\) | −81.8104 | + | 141.700i | −0.0818104 | + | 0.141700i | ||||
\(101\) | −797.556 | − | 1381.41i | −0.785741 | − | 1.36094i | −0.928555 | − | 0.371194i | \(-0.878949\pi\) |
0.142815 | − | 0.989749i | \(-0.454385\pi\) | |||||||
\(102\) | 106.135 | + | 183.831i | 0.103028 | + | 0.178450i | ||||
\(103\) | −1570.30 | −1.50219 | −0.751096 | − | 0.660193i | \(-0.770475\pi\) | ||||
−0.751096 | + | 0.660193i | \(0.770475\pi\) | |||||||
\(104\) | 75.3465 | − | 948.814i | 0.0710417 | − | 0.894604i | ||||
\(105\) | −884.764 | −0.822325 | ||||||||
\(106\) | −111.626 | − | 193.343i | −0.102284 | − | 0.177161i | ||||
\(107\) | 3.36651 | + | 5.83096i | 0.00304161 | + | 0.00526823i | 0.867542 | − | 0.497364i | \(-0.165698\pi\) |
−0.864501 | + | 0.502632i | \(0.832365\pi\) | |||||||
\(108\) | −78.9824 | + | 136.801i | −0.0703711 | + | 0.121886i | ||||
\(109\) | −542.422 | −0.476648 | −0.238324 | − | 0.971186i | \(-0.576598\pi\) | ||||
−0.238324 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(110\) | 338.848 | − | 586.903i | 0.293708 | − | 0.508718i | ||||
\(111\) | −48.6374 | + | 84.2425i | −0.0415897 | + | 0.0720355i | ||||
\(112\) | 509.969 | 0.430246 | ||||||||
\(113\) | 721.411 | − | 1249.52i | 0.600572 | − | 1.04022i | −0.392162 | − | 0.919896i | \(-0.628273\pi\) |
0.992735 | − | 0.120325i | \(-0.0383938\pi\) | |||||||
\(114\) | −264.558 | − | 458.229i | −0.217352 | − | 0.376465i | ||||
\(115\) | −643.719 | − | 1114.95i | −0.521975 | − | 0.904087i | ||||
\(116\) | 1140.54 | 0.912900 | ||||||||
\(117\) | 347.489 | + | 239.183i | 0.274576 | + | 0.188996i | ||||
\(118\) | −480.577 | −0.374921 | ||||||||
\(119\) | 722.467 | + | 1251.35i | 0.556542 | + | 0.963958i | ||||
\(120\) | 300.042 | + | 519.689i | 0.228250 | + | 0.395340i | ||||
\(121\) | −435.513 | + | 754.330i | −0.327207 | + | 0.566739i | ||||
\(122\) | 144.291 | 0.107078 | ||||||||
\(123\) | −362.738 | + | 628.280i | −0.265910 | + | 0.460570i | ||||
\(124\) | −93.6446 | + | 162.197i | −0.0678188 | + | 0.117466i | ||||
\(125\) | −1506.81 | −1.07818 | ||||||||
\(126\) | 197.525 | − | 342.124i | 0.139658 | − | 0.241895i | ||||
\(127\) | 1246.42 | + | 2158.86i | 0.870881 | + | 1.50841i | 0.861087 | + | 0.508458i | \(0.169784\pi\) |
0.00979442 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(128\) | −648.153 | − | 1122.63i | −0.447572 | − | 0.775217i | ||||
\(129\) | −289.226 | −0.197403 | ||||||||
\(130\) | 611.186 | − | 290.992i | 0.412343 | − | 0.196321i | ||||
\(131\) | 744.561 | 0.496585 | 0.248292 | − | 0.968685i | \(-0.420131\pi\) | ||||
0.248292 | + | 0.968685i | \(0.420131\pi\) | |||||||
\(132\) | −411.812 | − | 713.279i | −0.271543 | − | 0.470326i | ||||
\(133\) | −1800.87 | − | 3119.20i | −1.17410 | − | 2.03360i | ||||
\(134\) | −323.386 | + | 560.121i | −0.208480 | + | 0.361097i | ||||
\(135\) | −265.965 | −0.169560 | ||||||||
\(136\) | 490.008 | − | 848.718i | 0.308955 | − | 0.535125i | ||||
\(137\) | 111.083 | − | 192.402i | 0.0692736 | − | 0.119985i | −0.829308 | − | 0.558792i | \(-0.811265\pi\) |
0.898582 | + | 0.438806i | \(0.144599\pi\) | |||||||
\(138\) | 574.846 | 0.354595 | ||||||||
\(139\) | 388.573 | − | 673.028i | 0.237110 | − | 0.410687i | −0.722774 | − | 0.691085i | \(-0.757133\pi\) |
0.959884 | + | 0.280398i | \(0.0904665\pi\) | |||||||
\(140\) | 862.726 | + | 1494.28i | 0.520812 | + | 0.902072i | ||||
\(141\) | 808.522 | + | 1400.40i | 0.482907 | + | 0.836419i | ||||
\(142\) | −505.876 | −0.298959 | ||||||||
\(143\) | −1985.91 | + | 945.514i | −1.16133 | + | 0.552922i | ||||
\(144\) | 153.299 | 0.0887149 | ||||||||
\(145\) | 960.161 | + | 1663.05i | 0.549911 | + | 0.952473i | ||||
\(146\) | 567.263 | + | 982.529i | 0.321555 | + | 0.556950i | ||||
\(147\) | 830.070 | − | 1437.72i | 0.465735 | − | 0.806676i | ||||
\(148\) | 189.704 | 0.105362 | ||||||||
\(149\) | −889.147 | + | 1540.05i | −0.488871 | + | 0.846750i | −0.999918 | − | 0.0128032i | \(-0.995925\pi\) |
0.511047 | + | 0.859553i | \(0.329258\pi\) | |||||||
\(150\) | 61.5031 | − | 106.527i | 0.0334781 | − | 0.0579857i | ||||
\(151\) | 1166.00 | 0.628394 | 0.314197 | − | 0.949358i | \(-0.398265\pi\) | ||||
0.314197 | + | 0.949358i | \(0.398265\pi\) | |||||||
\(152\) | −1221.43 | + | 2115.57i | −0.651781 | + | 1.12892i | ||||
\(153\) | 217.177 | + | 376.162i | 0.114757 | + | 0.198764i | ||||
\(154\) | 1029.89 | + | 1783.82i | 0.538902 | + | 0.933407i | ||||
\(155\) | −315.338 | −0.163410 | ||||||||
\(156\) | 65.1253 | − | 820.102i | 0.0334244 | − | 0.420902i | ||||
\(157\) | 517.628 | 0.263129 | 0.131564 | − | 0.991308i | \(-0.458000\pi\) | ||||
0.131564 | + | 0.991308i | \(0.458000\pi\) | |||||||
\(158\) | −110.201 | − | 190.874i | −0.0554882 | − | 0.0961083i | ||||
\(159\) | −228.415 | − | 395.626i | −0.113928 | − | 0.197328i | ||||
\(160\) | 923.109 | − | 1598.87i | 0.456114 | − | 0.790012i | ||||
\(161\) | 3913.02 | 1.91546 | ||||||||
\(162\) | 59.3771 | − | 102.844i | 0.0287970 | − | 0.0498778i | ||||
\(163\) | −305.094 | + | 528.438i | −0.146606 | + | 0.253929i | −0.929971 | − | 0.367633i | \(-0.880168\pi\) |
0.783365 | + | 0.621562i | \(0.213502\pi\) | |||||||
\(164\) | 1414.81 | 0.673647 | ||||||||
\(165\) | 693.366 | − | 1200.95i | 0.327142 | − | 0.566627i | ||||
\(166\) | 247.746 | + | 429.109i | 0.115836 | + | 0.200635i | ||||
\(167\) | −1491.51 | − | 2583.36i | −0.691115 | − | 1.19705i | −0.971473 | − | 0.237150i | \(-0.923787\pi\) |
0.280358 | − | 0.959895i | \(-0.409547\pi\) | |||||||
\(168\) | −1823.89 | −0.837596 | ||||||||
\(169\) | −2169.46 | − | 346.747i | −0.987467 | − | 0.157827i | ||||
\(170\) | 696.990 | 0.314451 | ||||||||
\(171\) | −541.351 | − | 937.647i | −0.242094 | − | 0.419320i | ||||
\(172\) | 282.022 | + | 488.476i | 0.125023 | + | 0.216546i | ||||
\(173\) | −489.106 | + | 847.157i | −0.214948 | + | 0.372301i | −0.953257 | − | 0.302162i | \(-0.902292\pi\) |
0.738308 | + | 0.674463i | \(0.235625\pi\) | |||||||
\(174\) | −857.431 | −0.373573 | ||||||||
\(175\) | 418.657 | − | 725.134i | 0.180843 | − | 0.313229i | ||||
\(176\) | −399.649 | + | 692.213i | −0.171163 | + | 0.296463i | ||||
\(177\) | −983.377 | −0.417599 | ||||||||
\(178\) | 124.555 | − | 215.736i | 0.0524483 | − | 0.0908431i | ||||
\(179\) | −926.471 | − | 1604.69i | −0.386858 | − | 0.670058i | 0.605167 | − | 0.796099i | \(-0.293106\pi\) |
−0.992025 | + | 0.126040i | \(0.959773\pi\) | |||||||
\(180\) | 259.340 | + | 449.190i | 0.107389 | + | 0.186003i | ||||
\(181\) | 852.777 | 0.350201 | 0.175101 | − | 0.984551i | \(-0.443975\pi\) | ||||
0.175101 | + | 0.984551i | \(0.443975\pi\) | |||||||
\(182\) | −162.871 | + | 2050.97i | −0.0663339 | + | 0.835320i | ||||
\(183\) | 295.254 | 0.119267 | ||||||||
\(184\) | −1326.99 | − | 2298.41i | −0.531668 | − | 0.920875i | ||||
\(185\) | 159.702 | + | 276.612i | 0.0634676 | + | 0.109929i | ||||
\(186\) | 70.3999 | − | 121.936i | 0.0277525 | − | 0.0480688i | ||||
\(187\) | −2264.71 | −0.885627 | ||||||||
\(188\) | 1576.77 | − | 2731.04i | 0.611689 | − | 1.05948i | ||||
\(189\) | 404.185 | − | 700.068i | 0.155556 | − | 0.269431i | ||||
\(190\) | −1737.36 | −0.663377 | ||||||||
\(191\) | −2220.65 | + | 3846.27i | −0.841258 | + | 1.45710i | 0.0475730 | + | 0.998868i | \(0.484851\pi\) |
−0.888831 | + | 0.458234i | \(0.848482\pi\) | |||||||
\(192\) | 207.773 | + | 359.873i | 0.0780974 | + | 0.135269i | ||||
\(193\) | 1241.21 | + | 2149.85i | 0.462925 | + | 0.801810i | 0.999105 | − | 0.0422935i | \(-0.0134665\pi\) |
−0.536180 | + | 0.844104i | \(0.680133\pi\) | |||||||
\(194\) | −314.041 | −0.116221 | ||||||||
\(195\) | 1250.64 | − | 595.440i | 0.459281 | − | 0.218669i | ||||
\(196\) | −3237.57 | −1.17987 | ||||||||
\(197\) | −630.115 | − | 1091.39i | −0.227888 | − | 0.394713i | 0.729294 | − | 0.684200i | \(-0.239849\pi\) |
−0.957182 | + | 0.289487i | \(0.906515\pi\) | |||||||
\(198\) | 309.591 | + | 536.227i | 0.111119 | + | 0.192464i | ||||
\(199\) | 2760.48 | − | 4781.30i | 0.983344 | − | 1.70320i | 0.334266 | − | 0.942479i | \(-0.391511\pi\) |
0.649077 | − | 0.760722i | \(-0.275155\pi\) | |||||||
\(200\) | −567.901 | −0.200783 | ||||||||
\(201\) | −661.726 | + | 1146.14i | −0.232212 | + | 0.402202i | ||||
\(202\) | 1169.30 | − | 2025.28i | 0.407285 | − | 0.705438i | ||||
\(203\) | −5836.60 | −2.01798 | ||||||||
\(204\) | 423.535 | − | 733.585i | 0.145360 | − | 0.251771i | ||||
\(205\) | 1191.06 | + | 2062.97i | 0.405790 | + | 0.702849i | ||||
\(206\) | −1151.11 | − | 1993.78i | −0.389327 | − | 0.674334i | ||||
\(207\) | 1176.27 | 0.394960 | ||||||||
\(208\) | −720.853 | + | 343.206i | −0.240299 | + | 0.114409i | ||||
\(209\) | 5645.18 | 1.86835 | ||||||||
\(210\) | −648.577 | − | 1123.37i | −0.213124 | − | 0.369142i | ||||
\(211\) | 2263.90 | + | 3921.18i | 0.738640 | + | 1.27936i | 0.953108 | + | 0.302631i | \(0.0978649\pi\) |
−0.214468 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(212\) | −445.451 | + | 771.543i | −0.144310 | + | 0.249952i | ||||
\(213\) | −1035.15 | −0.332991 | ||||||||
\(214\) | −4.93564 | + | 8.54879i | −0.00157661 | + | 0.00273076i | ||||
\(215\) | −474.839 | + | 822.446i | −0.150622 | + | 0.260885i | ||||
\(216\) | −548.270 | −0.172709 | ||||||||
\(217\) | 479.217 | − | 830.029i | 0.149914 | − | 0.259659i | ||||
\(218\) | −397.623 | − | 688.703i | −0.123534 | − | 0.213967i | ||||
\(219\) | 1160.76 | + | 2010.49i | 0.358159 | + | 0.620349i | ||||
\(220\) | −2704.38 | −0.828770 | ||||||||
\(221\) | −1863.37 | − | 1282.60i | −0.567168 | − | 0.390393i | ||||
\(222\) | −142.615 | −0.0431157 | ||||||||
\(223\) | −2240.59 | − | 3880.81i | −0.672829 | − | 1.16537i | −0.977099 | − | 0.212787i | \(-0.931746\pi\) |
0.304270 | − | 0.952586i | \(-0.401588\pi\) | |||||||
\(224\) | 2805.68 | + | 4859.59i | 0.836887 | + | 1.44953i | ||||
\(225\) | 125.850 | − | 217.979i | 0.0372890 | − | 0.0645864i | ||||
\(226\) | 2115.32 | 0.622607 | ||||||||
\(227\) | 2879.88 | − | 4988.09i | 0.842044 | − | 1.45846i | −0.0461191 | − | 0.998936i | \(-0.514685\pi\) |
0.888163 | − | 0.459528i | \(-0.151981\pi\) | |||||||
\(228\) | −1055.73 | + | 1828.58i | −0.306656 | + | 0.531144i | ||||
\(229\) | −4635.08 | −1.33753 | −0.668766 | − | 0.743473i | \(-0.733177\pi\) | ||||
−0.668766 | + | 0.743473i | \(0.733177\pi\) | |||||||
\(230\) | 943.757 | − | 1634.64i | 0.270563 | − | 0.468629i | ||||
\(231\) | 2107.41 | + | 3650.14i | 0.600248 | + | 1.03966i | ||||
\(232\) | 1979.31 | + | 3428.27i | 0.560122 | + | 0.970160i | ||||
\(233\) | 5886.33 | 1.65505 | 0.827524 | − | 0.561431i | \(-0.189749\pi\) | ||||
0.827524 | + | 0.561431i | \(0.189749\pi\) | |||||||
\(234\) | −48.9597 | + | 616.533i | −0.0136778 | + | 0.172240i | ||||
\(235\) | 5309.59 | 1.47387 | ||||||||
\(236\) | 958.882 | + | 1660.83i | 0.264483 | + | 0.458097i | ||||
\(237\) | −225.498 | − | 390.574i | −0.0618046 | − | 0.107049i | ||||
\(238\) | −1059.21 | + | 1834.61i | −0.288481 | + | 0.499663i | ||||
\(239\) | 2135.84 | 0.578060 | 0.289030 | − | 0.957320i | \(-0.406667\pi\) | ||||
0.289030 | + | 0.957320i | \(0.406667\pi\) | |||||||
\(240\) | 251.680 | − | 435.923i | 0.0676912 | − | 0.117245i | ||||
\(241\) | −2346.46 | + | 4064.19i | −0.627173 | + | 1.08630i | 0.360943 | + | 0.932588i | \(0.382455\pi\) |
−0.988116 | + | 0.153708i | \(0.950879\pi\) | |||||||
\(242\) | −1277.01 | −0.339212 | ||||||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −287.899 | − | 498.656i | −0.0755364 | − | 0.130833i | ||||
\(245\) | −2725.55 | − | 4720.79i | −0.710730 | − | 1.23102i | ||||
\(246\) | −1063.62 | −0.275667 | ||||||||
\(247\) | 4644.77 | + | 3197.09i | 1.19652 | + | 0.823587i | ||||
\(248\) | −650.051 | −0.166445 | ||||||||
\(249\) | 506.949 | + | 878.062i | 0.129022 | + | 0.223473i | ||||
\(250\) | −1104.57 | − | 1913.16i | −0.279435 | − | 0.483996i | ||||
\(251\) | 1951.44 | − | 3379.99i | 0.490732 | − | 0.849973i | −0.509211 | − | 0.860642i | \(-0.670063\pi\) |
0.999943 | + | 0.0106687i | \(0.00339603\pi\) | |||||||
\(252\) | −1576.47 | −0.394080 | ||||||||
\(253\) | −3066.53 | + | 5311.38i | −0.762020 | + | 1.31986i | ||||
\(254\) | −1827.38 | + | 3165.11i | −0.451417 | + | 0.781877i | ||||
\(255\) | 1426.21 | 0.350246 | ||||||||
\(256\) | 1504.32 | − | 2605.56i | 0.367265 | − | 0.636122i | ||||
\(257\) | 2065.42 | + | 3577.40i | 0.501312 | + | 0.868297i | 0.999999 | + | 0.00151510i | \(0.000482272\pi\) |
−0.498687 | + | 0.866782i | \(0.666184\pi\) | |||||||
\(258\) | −212.017 | − | 367.225i | −0.0511614 | − | 0.0886141i | ||||
\(259\) | −970.790 | −0.232903 | ||||||||
\(260\) | −2225.13 | − | 1531.60i | −0.530756 | − | 0.365330i | ||||
\(261\) | −1754.51 | −0.416098 | ||||||||
\(262\) | 545.801 | + | 945.356i | 0.128701 | + | 0.222917i | ||||
\(263\) | −3176.09 | − | 5501.14i | −0.744661 | − | 1.28979i | −0.950353 | − | 0.311174i | \(-0.899278\pi\) |
0.205692 | − | 0.978617i | \(-0.434056\pi\) | |||||||
\(264\) | 1429.33 | − | 2475.68i | 0.333217 | − | 0.577149i | ||||
\(265\) | −1500.01 | −0.347716 | ||||||||
\(266\) | 2640.26 | − | 4573.06i | 0.608589 | − | 1.05411i | ||||
\(267\) | 254.870 | − | 441.448i | 0.0584187 | − | 0.101184i | ||||
\(268\) | 2580.97 | 0.588276 | ||||||||
\(269\) | −90.7619 | + | 157.204i | −0.0205719 | + | 0.0356316i | −0.876128 | − | 0.482078i | \(-0.839882\pi\) |
0.855556 | + | 0.517710i | \(0.173215\pi\) | |||||||
\(270\) | −194.966 | − | 337.690i | −0.0439453 | − | 0.0761155i | ||||
\(271\) | −1730.18 | − | 2996.75i | −0.387825 | − | 0.671733i | 0.604331 | − | 0.796733i | \(-0.293440\pi\) |
−0.992157 | + | 0.125000i | \(0.960107\pi\) | |||||||
\(272\) | −822.053 | −0.183251 | ||||||||
\(273\) | −333.273 | + | 4196.79i | −0.0738849 | + | 0.930408i | ||||
\(274\) | 325.719 | 0.0718153 | ||||||||
\(275\) | 656.180 | + | 1136.54i | 0.143888 | + | 0.249221i | ||||
\(276\) | −1146.97 | − | 1986.62i | −0.250144 | − | 0.433262i | ||||
\(277\) | 3218.97 | − | 5575.42i | 0.698228 | − | 1.20937i | −0.270853 | − | 0.962621i | \(-0.587306\pi\) |
0.969080 | − | 0.246745i | \(-0.0793611\pi\) | |||||||
\(278\) | 1139.37 | 0.245810 | ||||||||
\(279\) | 144.055 | − | 249.511i | 0.0309117 | − | 0.0535406i | ||||
\(280\) | −2994.38 | + | 5186.42i | −0.639102 | + | 1.10696i | ||||
\(281\) | −2974.26 | −0.631421 | −0.315711 | − | 0.948855i | \(-0.602243\pi\) | ||||
−0.315711 | + | 0.948855i | \(0.602243\pi\) | |||||||
\(282\) | −1185.38 | + | 2053.13i | −0.250312 | + | 0.433554i | ||||
\(283\) | −1517.86 | − | 2629.01i | −0.318825 | − | 0.552221i | 0.661418 | − | 0.750017i | \(-0.269955\pi\) |
−0.980243 | + | 0.197797i | \(0.936621\pi\) | |||||||
\(284\) | 1009.36 | + | 1748.27i | 0.210896 | + | 0.365283i | ||||
\(285\) | −3555.07 | −0.738891 | ||||||||
\(286\) | −2656.28 | − | 1828.37i | −0.549192 | − | 0.378020i | ||||
\(287\) | −7240.15 | −1.48910 | ||||||||
\(288\) | 843.403 | + | 1460.82i | 0.172563 | + | 0.298887i | ||||
\(289\) | 1291.91 | + | 2237.65i | 0.262957 | + | 0.455455i | ||||
\(290\) | −1407.69 | + | 2438.20i | −0.285044 | + | 0.493710i | ||||
\(291\) | −642.604 | −0.129451 | ||||||||
\(292\) | 2263.69 | − | 3920.83i | 0.453673 | − | 0.785784i | ||||
\(293\) | 977.872 | − | 1693.72i | 0.194976 | − | 0.337708i | −0.751917 | − | 0.659258i | \(-0.770871\pi\) |
0.946893 | + | 0.321550i | \(0.104204\pi\) | |||||||
\(294\) | 2433.93 | 0.482823 | ||||||||
\(295\) | −1614.47 | + | 2796.34i | −0.318637 | + | 0.551895i | ||||
\(296\) | 329.216 | + | 570.218i | 0.0646462 | + | 0.111970i | ||||
\(297\) | 633.498 | + | 1097.25i | 0.123769 | + | 0.214373i | ||||
\(298\) | −2607.16 | −0.506808 | ||||||||
\(299\) | −5531.15 | + | 2633.43i | −1.06981 | + | 0.509349i | ||||
\(300\) | −490.862 | −0.0944665 | ||||||||
\(301\) | −1443.22 | − | 2499.73i | −0.276365 | − | 0.478678i | ||||
\(302\) | 854.736 | + | 1480.45i | 0.162863 | + | 0.282086i | ||||
\(303\) | 2392.67 | − | 4144.22i | 0.453648 | − | 0.785741i | ||||
\(304\) | 2049.10 | 0.386593 | ||||||||
\(305\) | 484.735 | − | 839.586i | 0.0910029 | − | 0.157622i | ||||
\(306\) | −318.404 | + | 551.492i | −0.0594835 | + | 0.103028i | ||||
\(307\) | −1027.56 | −0.191029 | −0.0955147 | − | 0.995428i | \(-0.530450\pi\) | ||||
−0.0955147 | + | 0.995428i | \(0.530450\pi\) | |||||||
\(308\) | 4109.83 | − | 7118.43i | 0.760322 | − | 1.31692i | ||||
\(309\) | −2355.44 | − | 4079.75i | −0.433646 | − | 0.751096i | ||||
\(310\) | −231.159 | − | 400.379i | −0.0423515 | − | 0.0733549i | ||||
\(311\) | 3405.61 | 0.620947 | 0.310474 | − | 0.950582i | \(-0.399512\pi\) | ||||
0.310474 | + | 0.950582i | \(0.399512\pi\) | |||||||
\(312\) | 2578.11 | − | 1227.46i | 0.467810 | − | 0.222729i | ||||
\(313\) | 4813.20 | 0.869196 | 0.434598 | − | 0.900625i | \(-0.356890\pi\) | ||||
0.434598 | + | 0.900625i | \(0.356890\pi\) | |||||||
\(314\) | 379.447 | + | 657.222i | 0.0681957 | + | 0.118118i | ||||
\(315\) | −1327.15 | − | 2298.69i | −0.237385 | − | 0.411163i | ||||
\(316\) | −439.763 | + | 761.691i | −0.0782866 | + | 0.135596i | ||||
\(317\) | 1141.33 | 0.202219 | 0.101110 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101110 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(318\) | 334.879 | − | 580.028i | 0.0590538 | − | 0.102284i | ||||
\(319\) | 4573.99 | − | 7922.38i | 0.802803 | − | 1.39050i | ||||
\(320\) | 1364.45 | 0.238359 | ||||||||
\(321\) | −10.0995 | + | 17.4929i | −0.00175608 | + | 0.00304161i | ||||
\(322\) | 2868.44 | + | 4968.29i | 0.496435 | + | 0.859850i | ||||
\(323\) | 2902.94 | + | 5028.04i | 0.500074 | + | 0.866154i | ||||
\(324\) | −473.894 | −0.0812576 | ||||||||
\(325\) | −103.771 | + | 1306.75i | −0.0177113 | + | 0.223032i | ||||
\(326\) | −894.597 | −0.151985 | ||||||||
\(327\) | −813.633 | − | 1409.25i | −0.137596 | − | 0.238324i | ||||
\(328\) | 2455.29 | + | 4252.69i | 0.413325 | + | 0.715900i | ||||
\(329\) | −8068.94 | + | 13975.8i | −1.35214 | + | 2.34198i | ||||
\(330\) | 2033.09 | 0.339145 | ||||||||
\(331\) | −3826.28 | + | 6627.32i | −0.635382 | + | 1.10051i | 0.351052 | + | 0.936356i | \(0.385824\pi\) |
−0.986434 | + | 0.164158i | \(0.947509\pi\) | |||||||
\(332\) | 988.643 | − | 1712.38i | 0.163430 | − | 0.283069i | ||||
\(333\) | −291.825 | −0.0480237 | ||||||||
\(334\) | 2186.70 | − | 3787.47i | 0.358236 | − | 0.620483i | ||||
\(335\) | 2172.79 | + | 3763.38i | 0.354364 | + | 0.613777i | ||||
\(336\) | 764.953 | + | 1324.94i | 0.124201 | + | 0.215123i | ||||
\(337\) | −2503.69 | −0.404702 | −0.202351 | − | 0.979313i | \(-0.564858\pi\) | ||||
−0.202351 | + | 0.979313i | \(0.564858\pi\) | |||||||
\(338\) | −1150.07 | − | 3008.71i | −0.185076 | − | 0.484178i | ||||
\(339\) | 4328.47 | 0.693481 | ||||||||
\(340\) | −1390.68 | − | 2408.74i | −0.221825 | − | 0.384212i | ||||
\(341\) | 751.100 | + | 1300.94i | 0.119280 | + | 0.206598i | ||||
\(342\) | 793.675 | − | 1374.69i | 0.125488 | − | 0.217352i | ||||
\(343\) | 6298.69 | 0.991537 | ||||||||
\(344\) | −978.853 | + | 1695.42i | −0.153419 | + | 0.265730i | ||||
\(345\) | 1931.16 | − | 3344.86i | 0.301362 | − | 0.521975i | ||||
\(346\) | −1434.16 | −0.222835 | ||||||||
\(347\) | −2248.06 | + | 3893.75i | −0.347787 | + | 0.602385i | −0.985856 | − | 0.167594i | \(-0.946400\pi\) |
0.638069 | + | 0.769979i | \(0.279733\pi\) | |||||||
\(348\) | 1710.81 | + | 2963.21i | 0.263532 | + | 0.456450i | ||||
\(349\) | −1788.81 | − | 3098.31i | −0.274363 | − | 0.475211i | 0.695611 | − | 0.718418i | \(-0.255134\pi\) |
−0.969974 | + | 0.243208i | \(0.921800\pi\) | |||||||
\(350\) | 1227.59 | 0.187478 | ||||||||
\(351\) | −100.183 | + | 1261.58i | −0.0152348 | + | 0.191846i | ||||
\(352\) | −8794.96 | −1.33174 | ||||||||
\(353\) | 4022.58 | + | 6967.32i | 0.606517 | + | 1.05052i | 0.991810 | + | 0.127724i | \(0.0407672\pi\) |
−0.385293 | + | 0.922794i | \(0.625900\pi\) | |||||||
\(354\) | −720.865 | − | 1248.57i | −0.108230 | − | 0.187460i | ||||
\(355\) | −1699.46 | + | 2943.55i | −0.254079 | + | 0.440077i | ||||
\(356\) | −994.086 | −0.147996 | ||||||||
\(357\) | −2167.40 | + | 3754.05i | −0.321319 | + | 0.556542i | ||||
\(358\) | 1358.30 | − | 2352.64i | 0.200526 | − | 0.347322i | ||||
\(359\) | −2172.90 | −0.319447 | −0.159724 | − | 0.987162i | \(-0.551060\pi\) | ||||
−0.159724 | + | 0.987162i | \(0.551060\pi\) | |||||||
\(360\) | −900.127 | + | 1559.07i | −0.131780 | + | 0.228250i | ||||
\(361\) | −3806.57 | − | 6593.17i | −0.554974 | − | 0.961244i | ||||
\(362\) | 625.129 | + | 1082.75i | 0.0907625 | + | 0.157205i | ||||
\(363\) | −2613.08 | −0.377826 | ||||||||
\(364\) | 7412.96 | − | 3529.39i | 1.06743 | − | 0.508215i | ||||
\(365\) | 7622.74 | 1.09313 | ||||||||
\(366\) | 216.436 | + | 374.878i | 0.0309107 | + | 0.0535388i | ||||
\(367\) | −3831.38 | − | 6636.15i | −0.544949 | − | 0.943880i | −0.998610 | − | 0.0527056i | \(-0.983216\pi\) |
0.453661 | − | 0.891175i | \(-0.350118\pi\) | |||||||
\(368\) | −1113.10 | + | 1927.94i | −0.157675 | + | 0.273100i | ||||
\(369\) | −2176.43 | −0.307047 | ||||||||
\(370\) | −234.139 | + | 405.541i | −0.0328981 | + | 0.0569812i | ||||
\(371\) | 2279.55 | − | 3948.30i | 0.318998 | − | 0.552521i | ||||
\(372\) | −561.868 | −0.0783105 | ||||||||
\(373\) | −5271.27 | + | 9130.10i | −0.731732 | + | 1.26740i | 0.224411 | + | 0.974495i | \(0.427954\pi\) |
−0.956143 | + | 0.292902i | \(0.905379\pi\) | |||||||
\(374\) | −1660.15 | − | 2875.46i | −0.229530 | − | 0.397558i | ||||
\(375\) | −2260.21 | − | 3914.80i | −0.311244 | − | 0.539091i | ||||
\(376\) | 10945.4 | 1.50124 | ||||||||
\(377\) | 8250.17 | − | 3927.99i | 1.12707 | − | 0.536610i | ||||
\(378\) | 1185.15 | 0.161264 | ||||||||
\(379\) | −2737.77 | − | 4741.96i | −0.371055 | − | 0.642686i | 0.618673 | − | 0.785648i | \(-0.287671\pi\) |
−0.989728 | + | 0.142962i | \(0.954337\pi\) | |||||||
\(380\) | 3466.51 | + | 6004.18i | 0.467970 | + | 0.810547i | ||||
\(381\) | −3739.26 | + | 6476.59i | −0.502803 | + | 0.870881i | ||||
\(382\) | −6511.39 | −0.872124 | ||||||||
\(383\) | −404.042 | + | 699.822i | −0.0539050 | + | 0.0933661i | −0.891719 | − | 0.452590i | \(-0.850500\pi\) |
0.837814 | + | 0.545956i | \(0.183833\pi\) | |||||||
\(384\) | 1944.46 | − | 3367.90i | 0.258406 | − | 0.447572i | ||||
\(385\) | 13839.4 | 1.83200 | ||||||||
\(386\) | −1819.75 | + | 3151.89i | −0.239955 | + | 0.415614i | ||||
\(387\) | −433.839 | − | 751.432i | −0.0569852 | − | 0.0987013i | ||||
\(388\) | 626.597 | + | 1085.30i | 0.0819862 | + | 0.142004i | ||||
\(389\) | −7060.26 | −0.920230 | −0.460115 | − | 0.887859i | \(-0.652192\pi\) | ||||
−0.460115 | + | 0.887859i | \(0.652192\pi\) | |||||||
\(390\) | 1672.80 | + | 1151.42i | 0.217193 | + | 0.149499i | ||||
\(391\) | −6307.65 | −0.815836 | ||||||||
\(392\) | −5618.55 | − | 9731.62i | −0.723928 | − | 1.25388i | ||||
\(393\) | 1116.84 | + | 1934.43i | 0.143352 | + | 0.248292i | ||||
\(394\) | 923.813 | − | 1600.09i | 0.118124 | − | 0.204598i | ||||
\(395\) | −1480.85 | −0.188633 | ||||||||
\(396\) | 1235.44 | − | 2139.84i | 0.156775 | − | 0.271543i | ||||
\(397\) | 709.947 | − | 1229.66i | 0.0897511 | − | 0.155453i | −0.817655 | − | 0.575709i | \(-0.804726\pi\) |
0.907406 | + | 0.420255i | \(0.138060\pi\) | |||||||
\(398\) | 8094.29 | 1.01942 | ||||||||
\(399\) | 5402.61 | − | 9357.60i | 0.677867 | − | 1.17410i | ||||
\(400\) | 238.182 | + | 412.544i | 0.0297728 | + | 0.0515680i | ||||
\(401\) | −5335.37 | − | 9241.13i | −0.664428 | − | 1.15082i | −0.979440 | − | 0.201735i | \(-0.935342\pi\) |
0.315012 | − | 0.949088i | \(-0.397991\pi\) | |||||||
\(402\) | −1940.31 | −0.240732 | ||||||||
\(403\) | −118.782 | + | 1495.78i | −0.0146822 | + | 0.184888i | ||||
\(404\) | −9332.28 | −1.14925 | ||||||||
\(405\) | −398.947 | − | 690.997i | −0.0489478 | − | 0.0847800i | ||||
\(406\) | −4278.52 | − | 7410.62i | −0.523004 | − | 0.905869i | ||||
\(407\) | 760.782 | − | 1317.71i | 0.0926550 | − | 0.160483i | ||||
\(408\) | 2940.05 | 0.356750 | ||||||||
\(409\) | −3175.78 | + | 5500.61i | −0.383942 | + | 0.665007i | −0.991622 | − | 0.129175i | \(-0.958767\pi\) |
0.607680 | + | 0.794182i | \(0.292100\pi\) | |||||||
\(410\) | −1746.21 | + | 3024.52i | −0.210339 | + | 0.364318i | ||||
\(411\) | 666.500 | 0.0799903 | ||||||||
\(412\) | −4593.54 | + | 7956.25i | −0.549290 | + | 0.951399i | ||||
\(413\) | −4906.98 | − | 8499.15i | −0.584641 | − | 1.01263i | ||||
\(414\) | 862.268 | + | 1493.49i | 0.102363 | + | 0.177297i | ||||
\(415\) | 3329.15 | 0.393787 | ||||||||
\(416\) | −7236.37 | − | 4980.94i | −0.852866 | − | 0.587045i | ||||
\(417\) | 2331.44 | 0.273791 | ||||||||
\(418\) | 4138.20 | + | 7167.57i | 0.484225 | + | 0.838702i | ||||
\(419\) | −2808.94 | − | 4865.22i | −0.327507 | − | 0.567259i | 0.654509 | − | 0.756054i | \(-0.272875\pi\) |
−0.982017 | + | 0.188795i | \(0.939542\pi\) | |||||||
\(420\) | −2588.18 | + | 4482.85i | −0.300691 | + | 0.520812i | ||||
\(421\) | −1518.29 | −0.175765 | −0.0878825 | − | 0.996131i | \(-0.528010\pi\) | ||||
−0.0878825 | + | 0.996131i | \(0.528010\pi\) | |||||||
\(422\) | −3319.10 | + | 5748.85i | −0.382870 | + | 0.663151i | ||||
\(423\) | −2425.57 | + | 4201.20i | −0.278806 | + | 0.482907i | ||||
\(424\) | −3092.17 | −0.354173 | ||||||||
\(425\) | −674.860 | + | 1168.89i | −0.0770248 | + | 0.133411i | ||||
\(426\) | −758.815 | − | 1314.31i | −0.0863021 | − | 0.149480i | ||||
\(427\) | 1473.30 | + | 2551.83i | 0.166974 | + | 0.289207i | ||||
\(428\) | 39.3918 | 0.00444878 | ||||||||
\(429\) | −5435.39 | − | 3741.28i | −0.611709 | − | 0.421051i | ||||
\(430\) | −1392.33 | −0.156149 | ||||||||
\(431\) | 2485.07 | + | 4304.26i | 0.277730 | + | 0.481042i | 0.970820 | − | 0.239809i | \(-0.0770848\pi\) |
−0.693091 | + | 0.720850i | \(0.743751\pi\) | |||||||
\(432\) | 229.949 | + | 398.283i | 0.0256098 | + | 0.0443574i | ||||
\(433\) | 1649.36 | − | 2856.77i | 0.183055 | − | 0.317061i | −0.759864 | − | 0.650082i | \(-0.774735\pi\) |
0.942919 | + | 0.333021i | \(0.108068\pi\) | |||||||
\(434\) | 1405.16 | 0.155415 | ||||||||
\(435\) | −2880.48 | + | 4989.14i | −0.317491 | + | 0.549911i | ||||
\(436\) | −1586.73 | + | 2748.30i | −0.174291 | + | 0.301880i | ||||
\(437\) | 15722.9 | 1.72112 | ||||||||
\(438\) | −1701.79 | + | 2947.59i | −0.185650 | + | 0.321555i | ||||
\(439\) | 3024.24 | + | 5238.13i | 0.328790 | + | 0.569481i | 0.982272 | − | 0.187461i | \(-0.0600257\pi\) |
−0.653482 | + | 0.756942i | \(0.726692\pi\) | |||||||
\(440\) | −4693.24 | − | 8128.92i | −0.508503 | − | 0.880753i | ||||
\(441\) | 4980.42 | 0.537784 | ||||||||
\(442\) | 262.542 | − | 3306.10i | 0.0282530 | − | 0.355781i | ||||
\(443\) | 6822.62 | 0.731722 | 0.365861 | − | 0.930670i | \(-0.380775\pi\) | ||||
0.365861 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(444\) | 284.555 | + | 492.865i | 0.0304153 | + | 0.0526809i | ||||
\(445\) | −836.869 | − | 1449.50i | −0.0891493 | − | 0.154411i | ||||
\(446\) | 3284.93 | − | 5689.66i | 0.348757 | − | 0.604066i | ||||
\(447\) | −5334.88 | −0.564500 | ||||||||
\(448\) | −2073.54 | + | 3591.48i | −0.218673 | + | 0.378753i | ||||
\(449\) | −205.205 | + | 355.426i | −0.0215684 | + | 0.0373576i | −0.876608 | − | 0.481205i | \(-0.840199\pi\) |
0.855040 | + | 0.518563i | \(0.173533\pi\) | |||||||
\(450\) | 369.019 | 0.0386571 | ||||||||
\(451\) | 5673.91 | − | 9827.51i | 0.592404 | − | 1.02607i | ||||
\(452\) | −4220.65 | − | 7310.38i | −0.439209 | − | 0.760733i | ||||
\(453\) | 1749.00 | + | 3029.35i | 0.181402 | + | 0.314197i | ||||
\(454\) | 8444.38 | 0.872939 | ||||||||
\(455\) | 11386.9 | + | 7837.81i | 1.17324 | + | 0.807565i | ||||
\(456\) | −7328.56 | −0.752612 | ||||||||
\(457\) | 8321.41 | + | 14413.1i | 0.851771 | + | 1.47531i | 0.879609 | + | 0.475697i | \(0.157804\pi\) |
−0.0278385 | + | 0.999612i | \(0.508862\pi\) | |||||||
\(458\) | −3397.75 | − | 5885.07i | −0.346651 | − | 0.600418i | ||||
\(459\) | −651.532 | + | 1128.49i | −0.0662547 | + | 0.114757i | ||||
\(460\) | −7532.21 | −0.763459 | ||||||||
\(461\) | 5864.85 | − | 10158.2i | 0.592523 | − | 1.02628i | −0.401368 | − | 0.915917i | \(-0.631465\pi\) |
0.993891 | − | 0.110364i | \(-0.0352015\pi\) | |||||||
\(462\) | −3089.67 | + | 5351.47i | −0.311136 | + | 0.538902i | ||||
\(463\) | −3564.93 | −0.357832 | −0.178916 | − | 0.983864i | \(-0.557259\pi\) | ||||
−0.178916 | + | 0.983864i | \(0.557259\pi\) | |||||||
\(464\) | 1660.28 | − | 2875.69i | 0.166113 | − | 0.287717i | ||||
\(465\) | −473.008 | − | 819.273i | −0.0471725 | − | 0.0817051i | ||||
\(466\) | 4314.98 | + | 7473.76i | 0.428943 | + | 0.742951i | ||||
\(467\) | 1134.81 | 0.112447 | 0.0562233 | − | 0.998418i | \(-0.482094\pi\) | ||||
0.0562233 | + | 0.998418i | \(0.482094\pi\) | |||||||
\(468\) | 2228.37 | − | 1060.95i | 0.220100 | − | 0.104792i | ||||
\(469\) | −13207.9 | −1.30039 | ||||||||
\(470\) | 3892.20 | + | 6741.49i | 0.381987 | + | 0.661620i | ||||
\(471\) | 776.441 | + | 1344.84i | 0.0759587 | + | 0.131564i | ||||
\(472\) | −3328.12 | + | 5764.48i | −0.324554 | + | 0.562144i | ||||
\(473\) | 4524.05 | 0.439780 | ||||||||
\(474\) | 330.603 | − | 572.622i | 0.0320361 | − | 0.0554882i | ||||
\(475\) | 1682.20 | − | 2913.66i | 0.162494 | − | 0.281448i | ||||
\(476\) | 8453.65 | 0.814018 | ||||||||
\(477\) | 685.245 | − | 1186.88i | 0.0657761 | − | 0.113928i | ||||
\(478\) | 1565.68 | + | 2711.84i | 0.149817 | + | 0.259491i | ||||
\(479\) | 9686.30 | + | 16777.2i | 0.923963 | + | 1.60035i | 0.793220 | + | 0.608935i | \(0.208403\pi\) |
0.130743 | + | 0.991416i | \(0.458264\pi\) | |||||||
\(480\) | 5538.66 | 0.526675 | ||||||||
\(481\) | 1372.24 | − | 653.335i | 0.130080 | − | 0.0619325i | ||||
\(482\) | −6880.29 | −0.650184 | ||||||||
\(483\) | 5869.53 | + | 10166.3i | 0.552946 | + | 0.957730i | ||||
\(484\) | 2547.99 | + | 4413.24i | 0.239293 | + | 0.414467i | ||||
\(485\) | −1055.00 | + | 1827.31i | −0.0987733 | + | 0.171080i | ||||
\(486\) | 356.263 | 0.0332519 | ||||||||
\(487\) | 4522.98 | − | 7834.02i | 0.420853 | − | 0.728939i | −0.575170 | − | 0.818034i | \(-0.695064\pi\) |
0.996023 | + | 0.0890946i | \(0.0283973\pi\) | |||||||
\(488\) | 999.253 | − | 1730.76i | 0.0926927 | − | 0.160549i | ||||
\(489\) | −1830.56 | −0.169286 | ||||||||
\(490\) | 3995.93 | − | 6921.15i | 0.368403 | − | 0.638093i | ||||
\(491\) | −7201.66 | − | 12473.6i | −0.661927 | − | 1.14649i | −0.980109 | − | 0.198462i | \(-0.936405\pi\) |
0.318181 | − | 0.948030i | \(-0.396928\pi\) | |||||||
\(492\) | 2122.21 | + | 3675.78i | 0.194465 | + | 0.336823i | ||||
\(493\) | 9408.40 | 0.859499 | ||||||||
\(494\) | −654.429 | + | 8241.01i | −0.0596036 | + | 0.750568i | ||||
\(495\) | 4160.20 | 0.377751 | ||||||||
\(496\) | 272.637 | + | 472.221i | 0.0246809 | + | 0.0427486i | ||||
\(497\) | −5165.31 | − | 8946.58i | −0.466189 | − | 0.807463i | ||||
\(498\) | −743.239 | + | 1287.33i | −0.0668782 | + | 0.115836i | ||||
\(499\) | −9319.75 | −0.836091 | −0.418045 | − | 0.908426i | \(-0.637285\pi\) | ||||
−0.418045 | + | 0.908426i | \(0.637285\pi\) | |||||||
\(500\) | −4407.82 | + | 7634.57i | −0.394247 | + | 0.682856i | ||||
\(501\) | 4474.52 | − | 7750.09i | 0.399015 | − | 0.691115i | ||||
\(502\) | 5722.02 | 0.508737 | ||||||||
\(503\) | −1372.99 | + | 2378.09i | −0.121707 | + | 0.210802i | −0.920441 | − | 0.390882i | \(-0.872170\pi\) |
0.798734 | + | 0.601684i | \(0.205503\pi\) | |||||||
\(504\) | −2735.83 | − | 4738.60i | −0.241793 | − | 0.418798i | ||||
\(505\) | −7856.37 | − | 13607.6i | −0.692285 | − | 1.19907i | ||||
\(506\) | −8991.69 | −0.789979 | ||||||||
\(507\) | −2353.32 | − | 6156.55i | −0.206143 | − | 0.539294i | ||||
\(508\) | 14584.5 | 1.27378 | ||||||||
\(509\) | 591.055 | + | 1023.74i | 0.0514697 | + | 0.0891481i | 0.890612 | − | 0.454763i | \(-0.150276\pi\) |
−0.839143 | + | 0.543911i | \(0.816943\pi\) | |||||||
\(510\) | 1045.48 | + | 1810.83i | 0.0907742 | + | 0.157226i | ||||
\(511\) | −11584.2 | + | 20064.5i | −1.00285 | + | 1.73698i | ||||
\(512\) | −5959.48 | −0.514403 | ||||||||
\(513\) | 1624.05 | − | 2812.94i | 0.139773 | − | 0.242094i | ||||
\(514\) | −3028.11 | + | 5244.84i | −0.259852 | + | 0.450078i | ||||
\(515\) | −15468.3 | −1.32352 | ||||||||
\(516\) | −846.066 | + | 1465.43i | −0.0721821 | + | 0.125023i | ||||
\(517\) | −12646.8 | − | 21905.0i | −1.07584 | − | 1.86340i | ||||
\(518\) | −711.639 | − | 1232.59i | −0.0603622 | − | 0.104550i | ||||
\(519\) | −2934.64 | −0.248201 | ||||||||
\(520\) | 742.205 | − | 9346.33i | 0.0625920 | − | 0.788200i | ||||
\(521\) | 10858.8 | 0.913115 | 0.456558 | − | 0.889694i | \(-0.349082\pi\) | ||||
0.456558 | + | 0.889694i | \(0.349082\pi\) | |||||||
\(522\) | −1286.15 | − | 2227.67i | −0.107841 | − | 0.186786i | ||||
\(523\) | 5080.87 | + | 8800.33i | 0.424801 | + | 0.735777i | 0.996402 | − | 0.0847546i | \(-0.0270106\pi\) |
−0.571601 | + | 0.820532i | \(0.693677\pi\) | |||||||
\(524\) | 2178.05 | − | 3772.48i | 0.181581 | − | 0.314507i | ||||
\(525\) | 2511.94 | 0.208819 | ||||||||
\(526\) | 4656.47 | − | 8065.23i | 0.385992 | − | 0.668557i | ||||
\(527\) | −772.482 | + | 1337.98i | −0.0638517 | + | 0.110594i | ||||
\(528\) | −2397.89 | −0.197642 | ||||||||
\(529\) | −2457.36 | + | 4256.28i | −0.201970 | + | 0.349821i | ||||
\(530\) | −1099.58 | − | 1904.53i | −0.0901184 | − | 0.156090i | ||||
\(531\) | −1475.06 | − | 2554.89i | −0.120551 | − | 0.208800i | ||||
\(532\) | −21072.1 | −1.71728 | ||||||||
\(533\) | 10234.1 | − | 4872.57i | 0.831687 | − | 0.395975i | ||||
\(534\) | 747.331 | 0.0605621 | ||||||||
\(535\) | 33.1620 | + | 57.4382i | 0.00267984 | + | 0.00464162i | ||||
\(536\) | 4479.07 | + | 7757.98i | 0.360945 | + | 0.625175i | ||||
\(537\) | 2779.41 | − | 4814.08i | 0.223353 | − | 0.386858i | ||||
\(538\) | −266.132 | −0.0213267 | ||||||||
\(539\) | −12983.9 | + | 22488.7i | −1.03758 | + | 1.79714i | ||||
\(540\) | −778.019 | + | 1347.57i | −0.0620012 | + | 0.107389i | ||||
\(541\) | −9573.04 | −0.760771 | −0.380386 | − | 0.924828i | \(-0.624209\pi\) | ||||
−0.380386 | + | 0.924828i | \(0.624209\pi\) | |||||||
\(542\) | 2536.61 | − | 4393.54i | 0.201027 | − | 0.348190i | ||||
\(543\) | 1279.16 | + | 2215.58i | 0.101094 | + | 0.175101i | ||||
\(544\) | −4522.67 | − | 7833.49i | −0.356448 | − | 0.617386i | ||||
\(545\) | −5343.15 | −0.419955 | ||||||||
\(546\) | −5572.89 | + | 2653.31i | −0.436809 | + | 0.207969i | ||||
\(547\) | 15958.9 | 1.24745 | 0.623724 | − | 0.781645i | \(-0.285619\pi\) | ||||
0.623724 | + | 0.781645i | \(0.285619\pi\) | |||||||
\(548\) | −649.898 | − | 1125.66i | −0.0506611 | − | 0.0877475i | ||||
\(549\) | 442.881 | + | 767.092i | 0.0344293 | + | 0.0596333i | ||||
\(550\) | −962.027 | + | 1666.28i | −0.0745836 | + | 0.129183i | ||||
\(551\) | −23452.0 | −1.81323 | ||||||||
\(552\) | 3980.96 | − | 6895.23i | 0.306958 | − | 0.531668i | ||||
\(553\) | 2250.44 | − | 3897.88i | 0.173053 | − | 0.299737i | ||||
\(554\) | 9438.67 | 0.723846 | ||||||||
\(555\) | −479.105 | + | 829.835i | −0.0366430 | + | 0.0634676i | ||||
\(556\) | −2273.36 | − | 3937.58i | −0.173403 | − | 0.300343i | ||||
\(557\) | 1072.55 | + | 1857.70i | 0.0815892 | + | 0.141317i | 0.903933 | − | 0.427675i | \(-0.140667\pi\) |
−0.822344 | + | 0.568991i | \(0.807334\pi\) | |||||||
\(558\) | 422.399 | 0.0320459 | ||||||||
\(559\) | 3722.33 | + | 2562.15i | 0.281642 | + | 0.193859i | ||||
\(560\) | 5023.47 | 0.379072 | ||||||||
\(561\) | −3397.07 | − | 5883.90i | −0.255658 | − | 0.442813i | ||||
\(562\) | −2180.28 | − | 3776.36i | −0.163647 | − | 0.283445i | ||||
\(563\) | 11159.3 | − | 19328.5i | 0.835362 | − | 1.44689i | −0.0583740 | − | 0.998295i | \(-0.518592\pi\) |
0.893736 | − | 0.448594i | \(-0.148075\pi\) | |||||||
\(564\) | 9460.59 | 0.706317 | ||||||||
\(565\) | 7106.29 | − | 12308.5i | 0.529140 | − | 0.916497i | ||||
\(566\) | 2225.34 | − | 3854.40i | 0.165261 | − | 0.286241i | ||||
\(567\) | 2425.11 | 0.179621 | ||||||||
\(568\) | −3503.33 | + | 6067.95i | −0.258797 | + | 0.448249i | ||||
\(569\) | 9876.51 | + | 17106.6i | 0.727671 | + | 1.26036i | 0.957865 | + | 0.287218i | \(0.0927304\pi\) |
−0.230194 | + | 0.973145i | \(0.573936\pi\) | |||||||
\(570\) | −2606.05 | − | 4513.80i | −0.191500 | − | 0.331688i | ||||
\(571\) | −10640.6 | −0.779850 | −0.389925 | − | 0.920847i | \(-0.627499\pi\) | ||||
−0.389925 | + | 0.920847i | \(0.627499\pi\) | |||||||
\(572\) | −1018.69 | + | 12828.0i | −0.0744639 | + | 0.937699i | ||||
\(573\) | −13323.9 | −0.971401 | ||||||||
\(574\) | −5307.40 | − | 9192.69i | −0.385935 | − | 0.668459i | ||||
\(575\) | 1827.59 | + | 3165.47i | 0.132549 | + | 0.229581i | ||||
\(576\) | −623.318 | + | 1079.62i | −0.0450895 | + | 0.0780974i | ||||
\(577\) | 6547.89 | 0.472430 | 0.236215 | − | 0.971701i | \(-0.424093\pi\) | ||||
0.236215 | + | 0.971701i | \(0.424093\pi\) | |||||||
\(578\) | −1894.07 | + | 3280.62i | −0.136302 | + | 0.236083i | ||||
\(579\) | −3723.64 | + | 6449.54i | −0.267270 | + | 0.462925i | ||||
\(580\) | 11234.9 | 0.804319 | ||||||||
\(581\) | −5059.29 | + | 8762.94i | −0.361264 | + | 0.625728i | ||||
\(582\) | −471.061 | − | 815.902i | −0.0335500 | − | 0.0581104i | ||||
\(583\) | 3572.85 | + | 6188.35i | 0.253812 | + | 0.439615i | ||||
\(584\) | 15713.8 | 1.11343 | ||||||||
\(585\) | 3422.95 | + | 2356.09i | 0.241917 | + | 0.166517i | ||||
\(586\) | 2867.32 | 0.202130 | ||||||||
\(587\) | −2950.17 | − | 5109.84i | −0.207439 | − | 0.359294i | 0.743468 | − | 0.668771i | \(-0.233179\pi\) |
−0.950907 | + | 0.309477i | \(0.899846\pi\) | |||||||
\(588\) | −4856.36 | − | 8411.46i | −0.340600 | − | 0.589937i | ||||
\(589\) | 1925.54 | − | 3335.14i | 0.134704 | − | 0.233314i | ||||
\(590\) | −4733.94 | −0.330328 | ||||||||
\(591\) | 1890.35 | − | 3274.18i | 0.131571 | − | 0.227888i | ||||
\(592\) | 276.151 | − | 478.308i | 0.0191719 | − | 0.0332067i | ||||
\(593\) | −15261.5 | −1.05686 | −0.528428 | − | 0.848978i | \(-0.677218\pi\) | ||||
−0.528428 | + | 0.848978i | \(0.677218\pi\) | |||||||
\(594\) | −928.772 | + | 1608.68i | −0.0641548 | + | 0.111119i | ||||
\(595\) | 7116.70 | + | 12326.5i | 0.490346 | + | 0.849305i | ||||
\(596\) | 5202.00 | + | 9010.13i | 0.357520 | + | 0.619243i | ||||
\(597\) | 16562.9 | 1.13547 | ||||||||
\(598\) | −7398.23 | − | 5092.35i | −0.505913 | − | 0.348230i | ||||
\(599\) | −18900.6 | −1.28925 | −0.644623 | − | 0.764501i | \(-0.722986\pi\) | ||||
−0.644623 | + | 0.764501i | \(0.722986\pi\) | |||||||
\(600\) | −851.852 | − | 1475.45i | −0.0579612 | − | 0.100392i | ||||
\(601\) | 9253.48 | + | 16027.5i | 0.628049 | + | 1.08781i | 0.987943 | + | 0.154819i | \(0.0494794\pi\) |
−0.359894 | + | 0.932993i | \(0.617187\pi\) | |||||||
\(602\) | 2115.91 | − | 3664.86i | 0.143252 | − | 0.248120i | ||||
\(603\) | −3970.36 | −0.268135 | ||||||||
\(604\) | 3410.86 | − | 5907.79i | 0.229778 | − | 0.397987i | ||||
\(605\) | −4290.04 | + | 7430.56i | −0.288289 | + | 0.499331i | ||||
\(606\) | 7015.79 | 0.470292 | ||||||||
\(607\) | 3204.25 | − | 5549.92i | 0.214261 | − | 0.371111i | −0.738783 | − | 0.673944i | \(-0.764599\pi\) |
0.953044 | + | 0.302833i | \(0.0979324\pi\) | |||||||
\(608\) | 11273.5 | + | 19526.3i | 0.751976 | + | 1.30246i | ||||
\(609\) | −8754.90 | − | 15163.9i | −0.582539 | − | 1.00899i | ||||
\(610\) | 1421.34 | 0.0943418 | ||||||||
\(611\) | 2000.01 | − | 25185.5i | 0.132425 | − | 1.66759i | ||||
\(612\) | 2541.21 | 0.167847 | ||||||||
\(613\) | 1753.63 | + | 3037.38i | 0.115544 | + | 0.200128i | 0.917997 | − | 0.396587i | \(-0.129806\pi\) |
−0.802453 | + | 0.596715i | \(0.796472\pi\) | |||||||
\(614\) | −753.255 | − | 1304.68i | −0.0495096 | − | 0.0857532i | ||||
\(615\) | −3573.17 | + | 6188.91i | −0.234283 | + | 0.405790i | ||||
\(616\) | 28529.1 | 1.86602 | ||||||||
\(617\) | −7253.89 | + | 12564.1i | −0.473307 | + | 0.819792i | −0.999533 | − | 0.0305526i | \(-0.990273\pi\) |
0.526226 | + | 0.850345i | \(0.323607\pi\) | |||||||
\(618\) | 3453.32 | − | 5981.33i | 0.224778 | − | 0.389327i | ||||
\(619\) | 4750.85 | 0.308486 | 0.154243 | − | 0.988033i | \(-0.450706\pi\) | ||||
0.154243 | + | 0.988033i | \(0.450706\pi\) | |||||||
\(620\) | −922.451 | + | 1597.73i | −0.0597525 | + | 0.103494i | ||||
\(621\) | 1764.41 | + | 3056.05i | 0.114015 | + | 0.197480i | ||||
\(622\) | 2496.49 | + | 4324.04i | 0.160933 | + | 0.278743i | ||||
\(623\) | 5087.14 | 0.327146 | ||||||||
\(624\) | −1972.95 | − | 1358.02i | −0.126573 | − | 0.0871225i | ||||
\(625\) | −11347.0 | −0.726209 | ||||||||
\(626\) | 3528.32 | + | 6111.23i | 0.225272 | + | 0.390182i | ||||
\(627\) | 8467.76 | + | 14666.6i | 0.539346 | + | 0.934175i | ||||
\(628\) | 1514.20 | − | 2622.68i | 0.0962154 | − | 0.166650i | ||||
\(629\) | 1564.88 | 0.0991986 | ||||||||
\(630\) | 1945.73 | − | 3370.11i | 0.123047 | − | 0.213124i | ||||
\(631\) | −2412.60 | + | 4178.74i | −0.152209 | + | 0.263634i | −0.932039 | − | 0.362357i | \(-0.881972\pi\) |
0.779830 | + | 0.625991i | \(0.215305\pi\) | |||||||
\(632\) | −3052.69 | −0.192135 | ||||||||
\(633\) | −6791.69 | + | 11763.5i | −0.426454 | + | 0.738640i | ||||
\(634\) | 836.652 | + | 1449.12i | 0.0524096 | + | 0.0907762i | ||||
\(635\) | 12277.9 | + | 21266.0i | 0.767298 | + | 1.32900i | ||||
\(636\) | −2672.70 | −0.166635 | ||||||||
\(637\) | −23419.2 | + | 11150.1i | −1.45668 | + | 0.693539i | ||||
\(638\) | 13411.9 | 0.832258 | ||||||||
\(639\) | −1552.72 | − | 2689.39i | −0.0961262 | − | 0.166495i | ||||
\(640\) | −6384.66 | − | 11058.6i | −0.394337 | − | 0.683013i | ||||
\(641\) | 2955.95 | − | 5119.85i | 0.182142 | − | 0.315479i | −0.760468 | − | 0.649376i | \(-0.775030\pi\) |
0.942610 | + | 0.333897i | \(0.108364\pi\) | |||||||
\(642\) | −29.6139 | −0.00182051 | ||||||||
\(643\) | −11704.1 | + | 20272.2i | −0.717833 | + | 1.24332i | 0.244024 | + | 0.969769i | \(0.421532\pi\) |
−0.961857 | + | 0.273554i | \(0.911801\pi\) | |||||||
\(644\) | 11446.6 | − | 19826.2i | 0.700405 | − | 1.21314i | ||||
\(645\) | −2849.04 | −0.173924 | ||||||||
\(646\) | −4256.01 | + | 7371.62i | −0.259211 | + | 0.448967i | ||||
\(647\) | 8199.33 | + | 14201.7i | 0.498221 | + | 0.862944i | 0.999998 | − | 0.00205298i | \(-0.000653483\pi\) |
−0.501777 | + | 0.864997i | \(0.667320\pi\) | |||||||
\(648\) | −822.405 | − | 1424.45i | −0.0498567 | − | 0.0863543i | ||||
\(649\) | 15381.9 | 0.930342 | ||||||||
\(650\) | −1735.22 | + | 826.157i | −0.104709 | + | 0.0498532i | ||||
\(651\) | 2875.30 | 0.173106 | ||||||||
\(652\) | 1784.97 | + | 3091.65i | 0.107216 | + | 0.185703i | ||||
\(653\) | −13764.8 | − | 23841.3i | −0.824897 | − | 1.42876i | −0.901998 | − | 0.431741i | \(-0.857900\pi\) |
0.0771005 | − | 0.997023i | \(-0.475434\pi\) | |||||||
\(654\) | 1192.87 | − | 2066.11i | 0.0713224 | − | 0.123534i | ||||
\(655\) | 7334.34 | 0.437521 | ||||||||
\(656\) | 2059.54 | − | 3567.22i | 0.122578 | − | 0.212312i | ||||
\(657\) | −3482.28 | + | 6031.48i | −0.206783 | + | 0.358159i | ||||
\(658\) | −23659.8 | −1.40175 | ||||||||
\(659\) | 12089.9 | − | 20940.3i | 0.714650 | − | 1.23781i | −0.248444 | − | 0.968646i | \(-0.579919\pi\) |
0.963094 | − | 0.269164i | \(-0.0867474\pi\) | |||||||
\(660\) | −4056.57 | − | 7026.19i | −0.239245 | − | 0.414385i | ||||
\(661\) | −2262.52 | − | 3918.80i | −0.133134 | − | 0.230595i | 0.791749 | − | 0.610847i | \(-0.209171\pi\) |
−0.924883 | + | 0.380251i | \(0.875838\pi\) | |||||||
\(662\) | −11219.4 | −0.658695 | ||||||||
\(663\) | 537.224 | − | 6765.08i | 0.0314692 | − | 0.396281i | ||||
\(664\) | 6862.84 | 0.401099 | ||||||||
\(665\) | −17739.6 | − | 30725.8i | −1.03445 | − | 1.79172i | ||||
\(666\) | −213.922 | − | 370.524i | −0.0124464 | − | 0.0215578i | ||||
\(667\) | 12739.4 | − | 22065.3i | 0.739539 | − | 1.28092i | ||||
\(668\) | −17452.2 | −1.01085 | ||||||||
\(669\) | 6721.76 | − | 11642.4i | 0.388458 | − | 0.672829i | ||||
\(670\) | −3185.53 | + | 5517.49i | −0.183683 | + | 0.318148i | ||||
\(671\) | −4618.34 | −0.265706 | ||||||||
\(672\) | −8417.05 | + | 14578.8i | −0.483177 | + | 0.836887i | ||||
\(673\) | −1643.59 | − | 2846.78i | −0.0941393 | − | 0.163054i | 0.815110 | − | 0.579307i | \(-0.196677\pi\) |
−0.909249 | + | 0.416253i | \(0.863343\pi\) | |||||||
\(674\) | −1835.33 | − | 3178.89i | −0.104888 | − | 0.181671i | ||||
\(675\) | 755.102 | 0.0430576 | ||||||||
\(676\) | −8103.14 | + | 9977.74i | −0.461035 | + | 0.567691i | ||||
\(677\) | −9724.21 | −0.552041 | −0.276020 | − | 0.961152i | \(-0.589016\pi\) | ||||
−0.276020 | + | 0.961152i | \(0.589016\pi\) | |||||||
\(678\) | 3172.99 | + | 5495.77i | 0.179731 | + | 0.311304i | ||||
\(679\) | −3206.55 | − | 5553.91i | −0.181231 | − | 0.313902i | ||||
\(680\) | 4826.84 | − | 8360.34i | 0.272207 | − | 0.471477i | ||||
\(681\) | 17279.3 | 0.972309 | ||||||||
\(682\) | −1101.19 | + | 1907.31i | −0.0618280 | + | 0.107089i | ||||
\(683\) | −7274.33 | + | 12599.5i | −0.407532 | + | 0.705867i | −0.994613 | − | 0.103662i | \(-0.966944\pi\) |
0.587080 | + | 0.809529i | \(0.300277\pi\) | |||||||
\(684\) | −6334.40 | −0.354096 | ||||||||
\(685\) | 1094.23 | − | 1895.26i | 0.0610342 | − | 0.105714i | ||||
\(686\) | 4617.26 | + | 7997.33i | 0.256979 | + | 0.445101i | ||||
\(687\) | −6952.62 | − | 12042.3i | −0.386112 | − | 0.668766i | ||||
\(688\) | 1642.15 | 0.0909979 | ||||||||
\(689\) | −565.022 | + | 7115.13i | −0.0312418 | + | 0.393418i | ||||
\(690\) | 5662.54 | 0.312419 | ||||||||
\(691\) | −3364.48 | − | 5827.45i | −0.185226 | − | 0.320820i | 0.758427 | − | 0.651758i | \(-0.225968\pi\) |
−0.943653 | + | 0.330938i | \(0.892635\pi\) | |||||||
\(692\) | 2861.54 | + | 4956.33i | 0.157196 | + | 0.272271i | ||||
\(693\) | −6322.22 | + | 10950.4i | −0.346553 | + | 0.600248i | ||||
\(694\) | −6591.76 | −0.360548 | ||||||||
\(695\) | 3827.65 | − | 6629.69i | 0.208908 | − | 0.361839i | ||||
\(696\) | −5937.94 | + | 10284.8i | −0.323387 | + | 0.560122i | ||||
\(697\) | 11670.9 | 0.634241 | ||||||||
\(698\) | 2622.57 | − | 4542.43i | 0.142215 | − | 0.246323i | ||||
\(699\) | 8829.49 | + | 15293.1i | 0.477771 | + | 0.827524i | ||||
\(700\) | −2449.37 | − | 4242.43i | −0.132254 | − | 0.229070i | ||||
\(701\) | −29159.8 | −1.57111 | −0.785557 | − | 0.618789i | \(-0.787624\pi\) | ||||
−0.785557 | + | 0.618789i | \(0.787624\pi\) | |||||||
\(702\) | −1675.24 | + | 797.599i | −0.0900682 | + | 0.0428824i | ||||
\(703\) | −3900.73 | −0.209273 | ||||||||
\(704\) | −3249.96 | − | 5629.10i | −0.173988 | − | 0.301356i | ||||
\(705\) | 7964.39 | + | 13794.7i | 0.425470 | + | 0.736935i | ||||
\(706\) | −5897.52 | + | 10214.8i | −0.314385 | + | 0.544531i | ||||
\(707\) | 47757.0 | 2.54044 | ||||||||
\(708\) | −2876.64 | + | 4982.50i | −0.152699 | + | 0.264483i | ||||
\(709\) | 10244.5 | − | 17744.0i | 0.542653 | − | 0.939903i | −0.456097 | − | 0.889930i | \(-0.650753\pi\) |
0.998751 | − | 0.0499730i | \(-0.0159135\pi\) | |||||||
\(710\) | −4983.16 | −0.263401 | ||||||||
\(711\) | 676.495 | − | 1171.72i | 0.0356829 | − | 0.0618046i | ||||
\(712\) | −1725.16 | − | 2988.06i | −0.0908047 | − | 0.157278i | ||||
\(713\) | 2091.96 | + | 3623.37i | 0.109880 | + | 0.190318i | ||||
\(714\) | −6355.26 | −0.333109 | ||||||||
\(715\) | −19562.3 | + | 9313.83i | −1.02320 | + | 0.487157i | ||||
\(716\) | −10840.7 | −0.565833 | ||||||||
\(717\) | 3203.77 | + | 5549.09i | 0.166871 | + | 0.289030i | ||||
\(718\) | −1592.85 | − | 2758.90i | −0.0827919 | − | 0.143400i | ||||
\(719\) | 8995.06 | − | 15579.9i | 0.466563 | − | 0.808111i | −0.532707 | − | 0.846300i | \(-0.678825\pi\) |
0.999271 | + | 0.0381883i | \(0.0121587\pi\) | |||||||
\(720\) | 1510.08 | 0.0781631 | ||||||||
\(721\) | 23507.0 | − | 40715.3i | 1.21421 | − | 2.10308i | ||||
\(722\) | 5580.82 | − | 9666.26i | 0.287668 | − | 0.498256i | ||||
\(723\) | −14078.8 | −0.724197 | ||||||||
\(724\) | 2494.60 | − | 4320.78i | 0.128054 | − | 0.221796i | ||||
\(725\) | −2726.00 | − | 4721.57i | −0.139643 | − | 0.241869i | ||||
\(726\) | −1915.52 | − | 3317.77i | −0.0979222 | − | 0.169606i | ||||
\(727\) | −37652.7 | −1.92086 | −0.960428 | − | 0.278528i | \(-0.910153\pi\) | ||||
−0.960428 | + | 0.278528i | \(0.910153\pi\) | |||||||
\(728\) | 23473.4 | + | 16157.2i | 1.19503 | + | 0.822561i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5587.85 | + | 9678.45i | 0.283309 | + | 0.490706i | ||||
\(731\) | 2326.42 | + | 4029.48i | 0.117710 | + | 0.203879i | ||||
\(732\) | 863.698 | − | 1495.97i | 0.0436109 | − | 0.0755364i | ||||
\(733\) | 4524.26 | 0.227977 | 0.113989 | − | 0.993482i | \(-0.463637\pi\) | ||||
0.113989 | + | 0.993482i | \(0.463637\pi\) | |||||||
\(734\) | 5617.19 | − | 9729.26i | 0.282472 | − | 0.489256i | ||||
\(735\) | 8176.64 | − | 14162.4i | 0.410340 | − | 0.710730i | ||||
\(736\) | −24495.6 | −1.22679 | ||||||||
\(737\) | 10350.7 | − | 17927.9i | 0.517329 | − | 0.896040i | ||||
\(738\) | −1595.43 | − | 2763.37i | −0.0795781 | − | 0.137833i | ||||
\(739\) | −409.151 | − | 708.671i | −0.0203665 | − | 0.0352759i | 0.855663 | − | 0.517534i | \(-0.173150\pi\) |
−0.876029 | + | 0.482258i | \(0.839817\pi\) | |||||||
\(740\) | 1868.68 | 0.0928300 | ||||||||
\(741\) | −1339.12 | + | 16863.1i | −0.0663885 | + | 0.836008i | ||||
\(742\) | 6684.10 | 0.330702 | ||||||||
\(743\) | −19501.1 | − | 33776.9i | −0.962888 | − | 1.66777i | −0.715185 | − | 0.698935i | \(-0.753658\pi\) |
−0.247702 | − | 0.968836i | \(-0.579676\pi\) | |||||||
\(744\) | −975.077 | − | 1688.88i | −0.0480484 | − | 0.0832224i | ||||
\(745\) | −8758.59 | + | 15170.3i | −0.430725 | + | 0.746037i | ||||
\(746\) | −15456.4 | −0.758579 | ||||||||
\(747\) | −1520.85 | + | 2634.19i | −0.0744912 | + | 0.129022i | ||||
\(748\) | −6624.90 | + | 11474.7i | −0.323838 | + | 0.560903i | ||||
\(749\) | −201.584 | −0.00983407 | ||||||||
\(750\) | 3313.70 | − | 5739.49i | 0.161332 | − | 0.279435i | ||||
\(751\) | 11188.8 | + | 19379.7i | 0.543658 | + | 0.941643i | 0.998690 | + | 0.0511678i | \(0.0162943\pi\) |
−0.455032 | + | 0.890475i | \(0.650372\pi\) | |||||||
\(752\) | −4590.59 | − | 7951.13i | −0.222608 | − | 0.385569i | ||||
\(753\) | 11708.6 | 0.566649 | ||||||||
\(754\) | 11035.1 | + | 7595.67i | 0.532990 | + | 0.366868i | ||||
\(755\) | 11485.7 | 0.553653 | ||||||||
\(756\) | −2364.70 | − | 4095.78i | −0.113761 | − | 0.197040i | ||||
\(757\) | 17256.3 | + | 29888.8i | 0.828521 | + | 1.43504i | 0.899198 | + | 0.437542i | \(0.144151\pi\) |
−0.0706770 | + | 0.997499i | \(0.522516\pi\) | |||||||
\(758\) | 4013.85 | − | 6952.19i | 0.192335 | − | 0.333133i | ||||
\(759\) | −18399.2 | −0.879905 | ||||||||
\(760\) | −12031.7 | + | 20839.5i | −0.574258 | + | 0.994645i | ||||
\(761\) | −9987.78 | + | 17299.3i | −0.475764 | + | 0.824048i | −0.999615 | − | 0.0277624i | \(-0.991162\pi\) |
0.523850 | + | 0.851810i | \(0.324495\pi\) | |||||||
\(762\) | −10964.3 | −0.521251 | ||||||||
\(763\) | 8119.95 | − | 14064.2i | 0.385271 | − | 0.667309i | ||||
\(764\) | 12992.0 | + | 22502.8i | 0.615228 | + | 1.06561i | ||||
\(765\) | 2139.32 | + | 3705.40i | 0.101107 | + | 0.175123i | ||||
\(766\) | −1184.73 | −0.0558827 | ||||||||
\(767\) | 12656.0 | + | 8711.38i | 0.595804 | + | 0.410104i | ||||
\(768\) | 9025.91 | 0.424081 | ||||||||
\(769\) | 16532.4 | + | 28635.0i | 0.775260 | + | 1.34279i | 0.934648 | + | 0.355574i | \(0.115715\pi\) |
−0.159388 | + | 0.987216i | \(0.550952\pi\) | |||||||
\(770\) | 10145.0 | + | 17571.6i | 0.474805 | + | 0.822387i | ||||
\(771\) | −6196.25 | + | 10732.2i | −0.289432 | + | 0.501312i | ||||
\(772\) | 14523.6 | 0.677091 | ||||||||
\(773\) | 9282.01 | − | 16076.9i | 0.431890 | − | 0.748055i | −0.565146 | − | 0.824991i | \(-0.691180\pi\) |
0.997036 | + | 0.0769359i | \(0.0245137\pi\) | |||||||
\(774\) | 636.052 | − | 1101.68i | 0.0295380 | − | 0.0511614i | ||||
\(775\) | 895.279 | 0.0414960 | ||||||||
\(776\) | −2174.82 | + | 3766.90i | −0.100608 | + | 0.174257i | ||||
\(777\) | −1456.19 | − | 2522.19i | −0.0672334 | − | 0.116452i | ||||
\(778\) | −5175.53 | − | 8964.28i | −0.238498 | − | 0.413091i | ||||
\(779\) | −29091.6 | −1.33802 | ||||||||
\(780\) | 641.520 | − | 8078.45i | 0.0294489 | − | 0.370840i | ||||
\(781\) | 16191.7 | 0.741848 | ||||||||
\(782\) | −4623.83 | − | 8008.71i | −0.211442 | − | 0.366229i | ||||
\(783\) | −2631.77 | − | 4558.36i | −0.120117 | − | 0.208049i | ||||
\(784\) | −4712.93 | + | 8163.04i | −0.214693 | + | 0.371858i | ||||
\(785\) | 5098.91 | 0.231832 | ||||||||
\(786\) | −1637.40 | + | 2836.07i | −0.0743057 | + | 0.128701i | ||||
\(787\) | −18218.4 | + | 31555.2i | −0.825179 | + | 1.42925i | 0.0766032 | + | 0.997062i | \(0.475593\pi\) |
−0.901782 | + | 0.432190i | \(0.857741\pi\) | |||||||
\(788\) | −7373.04 | −0.333317 | ||||||||
\(789\) | 9528.26 | − | 16503.4i | 0.429930 | − | 0.744661i | ||||
\(790\) | −1085.54 | − | 1880.21i | −0.0488884 | − | 0.0846772i | ||||
\(791\) | 21598.8 | + | 37410.2i | 0.970877 | + | 1.68161i | ||||
\(792\) | 8576.00 | 0.384766 | ||||||||
\(793\) | −3799.90 | − | 2615.55i | −0.170162 | − | 0.117126i | ||||
\(794\) | 2081.71 | 0.0930441 | ||||||||
\(795\) | −2250.01 | − | 3897.13i | −0.100377 | − | 0.173858i | ||||
\(796\) | −16150.3 | − | 27973.2i | −0.719137 | − | 1.24558i | ||||
\(797\) | −6182.80 | + | 10708.9i | −0.274788 | + | 0.475947i | −0.970082 | − | 0.242779i | \(-0.921941\pi\) |
0.695294 | + | 0.718726i | \(0.255274\pi\) | |||||||
\(798\) | 15841.6 | 0.702738 | ||||||||
\(799\) | 13006.9 | − | 22528.6i | 0.575907 | − | 0.997501i | ||||
\(800\) | −2620.80 | + | 4539.37i | −0.115824 | + | 0.200614i | ||||
\(801\) | 1529.22 | 0.0674561 | ||||||||
\(802\) | 7822.19 | − | 13548.4i | 0.344403 | − | 0.596523i | ||||
\(803\) | −18156.5 | − | 31448.0i | −0.797918 | − | 1.38204i | ||||
\(804\) | 3871.46 | + | 6705.56i | 0.169821 | + | 0.294138i | ||||
\(805\) | 38545.4 | 1.68763 | ||||||||
\(806\) | −1986.23 | + | 945.665i | −0.0868015 | + | 0.0413271i | ||||
\(807\) | −544.571 | −0.0237544 | ||||||||
\(808\) | −16195.4 | − | 28051.3i | −0.705140 | − | 1.22134i | ||||
\(809\) | 4046.87 | + | 7009.39i | 0.175872 | + | 0.304619i | 0.940463 | − | 0.339897i | \(-0.110392\pi\) |
−0.764591 | + | 0.644516i | \(0.777059\pi\) | |||||||
\(810\) | 584.897 | − | 1013.07i | 0.0253718 | − | 0.0439453i | ||||
\(811\) | 15984.7 | 0.692105 | 0.346052 | − | 0.938215i | \(-0.387522\pi\) | ||||
0.346052 | + | 0.938215i | \(0.387522\pi\) | |||||||
\(812\) | −17073.6 | + | 29572.4i | −0.737891 | + | 1.27806i | ||||
\(813\) | 5190.53 | − | 8990.26i | 0.223911 | − | 0.387825i | ||||
\(814\) | 2230.77 | 0.0960546 | ||||||||
\(815\) | −3005.34 | + | 5205.40i | −0.129169 | + | 0.223727i | ||||
\(816\) | −1233.08 | − | 2135.76i | −0.0529000 | − | 0.0916255i | ||||
\(817\) | −5798.99 | − | 10044.2i | −0.248325 | − | 0.430111i | ||||
\(818\) | −9312.03 | −0.398029 | ||||||||
\(819\) | −11403.5 | + | 5429.32i | −0.486533 | + | 0.231643i | ||||
\(820\) | 13936.6 | 0.593523 | ||||||||
\(821\) | 13430.9 | + | 23263.1i | 0.570942 | + | 0.988900i | 0.996470 | + | 0.0839550i | \(0.0267552\pi\) |
−0.425528 | + | 0.904945i | \(0.639911\pi\) | |||||||
\(822\) | 488.578 | + | 846.242i | 0.0207313 | + | 0.0359076i | ||||
\(823\) | 2602.97 | − | 4508.48i | 0.110248 | − | 0.190955i | −0.805622 | − | 0.592429i | \(-0.798169\pi\) |
0.915870 | + | 0.401475i | \(0.131502\pi\) | |||||||
\(824\) | −31886.9 | −1.34810 | ||||||||
\(825\) | −1968.54 | + | 3409.61i | −0.0830737 | + | 0.143888i | ||||
\(826\) | 7194.14 | − | 12460.6i | 0.303046 | − | 0.524891i | ||||
\(827\) | 46621.5 | 1.96032 | 0.980162 | − | 0.198200i | \(-0.0635095\pi\) | ||||
0.980162 | + | 0.198200i | \(0.0635095\pi\) | |||||||
\(828\) | 3440.92 | − | 5959.85i | 0.144421 | − | 0.250144i | ||||
\(829\) | 20914.9 | + | 36225.6i | 0.876241 | + | 1.51769i | 0.855435 | + | 0.517910i | \(0.173290\pi\) |
0.0208053 | + | 0.999784i | \(0.493377\pi\) | |||||||
\(830\) | 2440.44 | + | 4226.96i | 0.102059 | + | 0.176771i | ||||
\(831\) | 19313.8 | 0.806244 | ||||||||
\(832\) | 513.960 | − | 6472.12i | 0.0214163 | − | 0.269688i | ||||
\(833\) | −26707.0 | −1.11086 | ||||||||
\(834\) | 1709.06 | + | 2960.18i | 0.0709592 | + | 0.122905i | ||||
\(835\) | −14692.1 | − | 25447.5i | −0.608913 | − | 1.05467i | ||||
\(836\) | 16513.7 | − | 28602.5i | 0.683179 | − | 1.18330i | ||||
\(837\) | 864.331 | 0.0356937 | ||||||||
\(838\) | 4118.19 | − | 7132.91i | 0.169762 | − | 0.294036i | ||||
\(839\) | −6342.54 | + | 10985.6i | −0.260988 | + | 0.452044i | −0.966505 | − | 0.256649i | \(-0.917382\pi\) |
0.705517 | + | 0.708693i | \(0.250715\pi\) | |||||||
\(840\) | −17966.3 | −0.737972 | ||||||||
\(841\) | −6807.43 | + | 11790.8i | −0.279119 | + | 0.483448i | ||||
\(842\) | −1112.99 | − | 1927.75i | −0.0455535 | − | 0.0789009i | ||||
\(843\) | −4461.39 | − | 7727.35i | −0.182276 | − | 0.315711i | ||||
\(844\) | 26490.1 | 1.08036 | ||||||||
\(845\) | −21370.4 | − | 3415.64i | −0.870017 | − | 0.139055i | ||||
\(846\) | −7112.25 | −0.289036 | ||||||||
\(847\) | −13039.1 | − | 22584.3i | −0.528959 | − | 0.916183i | ||||
\(848\) | 1296.88 | + | 2246.27i | 0.0525179 | + | 0.0909636i | ||||
\(849\) | 4553.58 | − | 7887.03i | 0.184074 | − | 0.318825i | ||||
\(850\) | −1978.83 | −0.0798509 | ||||||||
\(851\) | 2118.92 | − | 3670.08i | 0.0853534 | − | 0.147836i | ||||
\(852\) | −3028.08 | + | 5244.80i | −0.121761 | + | 0.210896i | ||||
\(853\) | −37493.3 | −1.50498 | −0.752488 | − | 0.658606i | \(-0.771146\pi\) | ||||
−0.752488 | + | 0.658606i | \(0.771146\pi\) | |||||||
\(854\) | −2160.00 | + | 3741.24i | −0.0865501 | + | 0.149909i | ||||
\(855\) | −5332.60 | − | 9236.34i | −0.213300 | − | 0.369446i | ||||
\(856\) | 68.3614 | + | 118.405i | 0.00272961 | + | 0.00472782i | ||||
\(857\) | −11826.3 | −0.471386 | −0.235693 | − | 0.971828i | \(-0.575736\pi\) | ||||
−0.235693 | + | 0.971828i | \(0.575736\pi\) | |||||||
\(858\) | 765.824 | − | 9643.76i | 0.0304718 | − | 0.383721i | ||||
\(859\) | −36498.7 | −1.44973 | −0.724866 | − | 0.688890i | \(-0.758099\pi\) | ||||
−0.724866 | + | 0.688890i | \(0.758099\pi\) | |||||||
\(860\) | 2778.07 | + | 4811.76i | 0.110153 | + | 0.190790i | ||||
\(861\) | −10860.2 | − | 18810.5i | −0.429867 | − | 0.744552i | ||||
\(862\) | −3643.36 | + | 6310.48i | −0.143960 | + | 0.249346i | ||||
\(863\) | 2292.79 | 0.0904372 | 0.0452186 | − | 0.998977i | \(-0.485602\pi\) | ||||
0.0452186 | + | 0.998977i | \(0.485602\pi\) | |||||||
\(864\) | −2530.21 | + | 4382.45i | −0.0996290 | + | 0.172563i | ||||
\(865\) | −4817.96 | + | 8344.95i | −0.189382 | + | 0.328020i | ||||
\(866\) | 4836.24 | 0.189772 | ||||||||
\(867\) | −3875.72 | + | 6712.95i | −0.151818 | + | 0.262957i | ||||
\(868\) | −2803.68 | − | 4856.12i | −0.109635 | − | 0.189893i | ||||
\(869\) | 3527.22 | + | 6109.33i | 0.137690 | + | 0.238487i | ||||
\(870\) | −8446.16 | −0.329140 | ||||||||
\(871\) | 18669.6 | − | 8888.81i | 0.726288 | − | 0.345793i | ||||
\(872\) | −11014.6 | −0.427753 | ||||||||
\(873\) | −963.906 | − | 1669.53i | −0.0373691 | − | 0.0647253i | ||||
\(874\) | 11525.7 | + | 19963.1i | 0.446066 | + | 0.772609i | ||||
\(875\) | 22556.6 | − | 39069.2i | 0.871488 | − | 1.50946i | ||||
\(876\) | 13582.1 | 0.523856 | ||||||||
\(877\) | 10400.1 | − | 18013.6i | 0.400442 | − | 0.693587i | −0.593337 | − | 0.804954i | \(-0.702190\pi\) |
0.993779 | + | 0.111368i | \(0.0355231\pi\) | |||||||
\(878\) | −4433.84 | + | 7679.63i | −0.170427 | + | 0.295188i | ||||
\(879\) | 5867.23 | 0.225139 | ||||||||
\(880\) | −3936.76 | + | 6818.67i | −0.150805 | + | 0.261202i | ||||
\(881\) | 9627.95 | + | 16676.1i | 0.368188 | + | 0.637721i | 0.989282 | − | 0.146015i | \(-0.0466448\pi\) |
−0.621094 | + | 0.783736i | \(0.713311\pi\) | |||||||
\(882\) | 3650.90 | + | 6323.54i | 0.139379 | + | 0.241411i | ||||
\(883\) | 1744.49 | 0.0664857 | 0.0332429 | − | 0.999447i | \(-0.489417\pi\) | ||||
0.0332429 | + | 0.999447i | \(0.489417\pi\) | |||||||
\(884\) | −11949.4 | + | 5689.25i | −0.454642 | + | 0.216460i | ||||
\(885\) | −9686.80 | −0.367930 | ||||||||
\(886\) | 5001.33 | + | 8662.56i | 0.189642 | + | 0.328470i | ||||
\(887\) | −1485.35 | − | 2572.70i | −0.0562268 | − | 0.0973877i | 0.836542 | − | 0.547903i | \(-0.184574\pi\) |
−0.892769 | + | 0.450515i | \(0.851240\pi\) | |||||||
\(888\) | −987.647 | + | 1710.65i | −0.0373235 | + | 0.0646462i | ||||
\(889\) | −74634.6 | −2.81571 | ||||||||
\(890\) | 1226.94 | − | 2125.11i | 0.0462101 | − | 0.0800382i | ||||
\(891\) | −1900.49 | + | 3291.75i | −0.0714578 | + | 0.123769i | ||||
\(892\) | −26217.3 | −0.984104 | ||||||||
\(893\) | −32421.8 | + | 56156.2i | −1.21495 | + | 2.10436i | ||||
\(894\) | −3910.74 | − | 6773.60i | −0.146303 | − | 0.253404i | ||||
\(895\) | −9126.24 | − | 15807.1i | −0.340845 | − | 0.590361i | ||||
\(896\) | 38810.9 | 1.44708 | ||||||||
\(897\) | −15138.6 | − | 10420.2i | −0.563503 | − | 0.387871i | ||||
\(898\) | −601.703 | −0.0223598 | ||||||||
\(899\) | −3120.33 | − | 5404.57i | −0.115761 | − | 0.200503i | ||||
\(900\) | −736.293 | − | 1275.30i | −0.0272701 | − | 0.0472332i | ||||
\(901\) | −3674.56 | + | 6364.52i | −0.135868 | + | 0.235331i | ||||
\(902\) | 16637.1 | 0.614140 | ||||||||
\(903\) | 4329.66 | − | 7499.19i | 0.159559 | − | 0.276365i | ||||
\(904\) | 14649.2 | − | 25373.2i | 0.538966 | − | 0.933516i | ||||
\(905\) | 8400.32 | 0.308548 | ||||||||
\(906\) | −2564.21 | + | 4441.34i | −0.0940288 | + | 0.162863i | ||||
\(907\) | −16501.7 | − | 28581.7i | −0.604111 | − | 1.04635i | −0.992191 | − | 0.124726i | \(-0.960195\pi\) |
0.388080 | − | 0.921626i | \(-0.373138\pi\) | |||||||
\(908\) | −16848.8 | − | 29183.1i | −0.615802 | − | 1.06660i | ||||
\(909\) | 14356.0 | 0.523827 | ||||||||
\(910\) | −1604.36 | + | 20203.2i | −0.0584441 | + | 0.735967i | ||||
\(911\) | 14977.0 | 0.544686 | 0.272343 | − | 0.962200i | \(-0.412201\pi\) | ||||
0.272343 | + | 0.962200i | \(0.412201\pi\) | |||||||
\(912\) | 3073.66 | + | 5323.73i | 0.111600 | + | 0.193296i | ||||
\(913\) | −7929.66 | − | 13734.6i | −0.287441 | − | 0.497862i | ||||
\(914\) | −12200.0 | + | 21131.1i | −0.441511 | + | 0.764720i | ||||
\(915\) | 2908.41 | 0.105081 | ||||||||
\(916\) | −13558.9 | + | 23484.7i | −0.489080 | + | 0.847112i | ||||
\(917\) | −11145.9 | + | 19305.3i | −0.401386 | + | 0.695221i | ||||
\(918\) | −1910.42 | −0.0686856 | ||||||||
\(919\) | −5712.69 | + | 9894.67i | −0.205054 | + | 0.355163i | −0.950150 | − | 0.311794i | \(-0.899070\pi\) |
0.745096 | + | 0.666957i | \(0.232404\pi\) | |||||||
\(920\) | −13071.6 | − | 22640.6i | −0.468431 | − | 0.811346i | ||||
\(921\) | −1541.34 | − | 2669.68i | −0.0551455 | − | 0.0955147i | ||||
\(922\) | 17196.9 | 0.614263 | ||||||||
\(923\) | 13322.3 | + | 9169.99i | 0.475090 | + | 0.327014i | ||||
\(924\) | 24659.0 | 0.877944 | ||||||||
\(925\) | −453.410 | − | 785.329i | −0.0161168 | − | 0.0279151i | ||||
\(926\) | −2613.27 | − | 4526.32i | −0.0927403 | − | 0.160631i | ||||
\(927\) | 7066.33 | − | 12239.2i | 0.250365 | − | 0.433646i | ||||
\(928\) | 36537.3 | 1.29245 | ||||||||
\(929\) | −5977.10 | + | 10352.6i | −0.211090 | + | 0.365618i | −0.952056 | − | 0.305924i | \(-0.901035\pi\) |
0.740966 | + | 0.671542i | \(0.234368\pi\) | |||||||
\(930\) | 693.477 | − | 1201.14i | 0.0244516 | − | 0.0423515i | ||||
\(931\) | 66571.7 | 2.34350 | ||||||||
\(932\) | 17219.1 | − | 29824.4i | 0.605183 | − | 1.04821i | ||||
\(933\) | 5108.42 | + | 8848.04i | 0.179252 | + | 0.310474i | ||||
\(934\) | 831.870 | + | 1440.84i | 0.0291431 | + | 0.0504773i | ||||
\(935\) | −22308.7 | −0.780290 | ||||||||
\(936\) | 7056.21 | + | 4856.93i | 0.246410 | + | 0.169609i | ||||
\(937\) | 42546.4 | 1.48338 | 0.741692 | − | 0.670740i | \(-0.234024\pi\) | ||||
0.741692 | + | 0.670740i | \(0.234024\pi\) | |||||||
\(938\) | −9682.04 | − | 16769.8i | −0.337025 | − | 0.583745i | ||||
\(939\) | 7219.81 | + | 12505.1i | 0.250915 | + | 0.434598i | ||||
\(940\) | 15532.0 | − | 26902.2i | 0.538934 | − | 0.933461i | ||||
\(941\) | 20665.1 | 0.715903 | 0.357951 | − | 0.933740i | \(-0.383475\pi\) | ||||
0.357951 | + | 0.933740i | \(0.383475\pi\) | |||||||
\(942\) | −1138.34 | + | 1971.67i | −0.0393728 | + | 0.0681957i | ||||
\(943\) | 15802.9 | − | 27371.5i | 0.545720 | − | 0.945215i | ||||
\(944\) | 5583.37 | 0.192503 | ||||||||
\(945\) | 3981.44 | − | 6896.06i | 0.137054 | − | 0.237385i | ||||
\(946\) | 3316.36 | + | 5744.10i | 0.113979 | + | 0.197417i | ||||
\(947\) | 4746.87 | + | 8221.81i | 0.162885 | + | 0.282126i | 0.935902 | − | 0.352260i | \(-0.114587\pi\) |
−0.773017 | + | 0.634385i | \(0.781253\pi\) | |||||||
\(948\) | −2638.58 | −0.0903976 | ||||||||
\(949\) | 2871.33 | − | 36157.7i | 0.0982163 | − | 1.23681i | ||||
\(950\) | 4932.56 | 0.168456 | ||||||||
\(951\) | 1711.99 | + | 2965.26i | 0.0583756 | + | 0.101110i | ||||
\(952\) | 14670.6 | + | 25410.3i | 0.499452 | + | 0.865076i | ||||
\(953\) | −26667.1 | + | 46188.7i | −0.906433 | + | 1.56999i | −0.0874512 | + | 0.996169i | \(0.527872\pi\) |
−0.818982 | + | 0.573819i | \(0.805461\pi\) | |||||||
\(954\) | 2009.28 | 0.0681894 | ||||||||
\(955\) | −21874.6 | + | 37887.9i | −0.741199 | + | 1.28379i | ||||
\(956\) | 6247.93 | − | 10821.7i | 0.211373 | − | 0.366108i | ||||
\(957\) | 27443.9 | 0.926997 | ||||||||
\(958\) | −14201.1 | + | 24597.0i | −0.478932 | + | 0.829534i | ||||
\(959\) | 3325.79 | + | 5760.44i | 0.111987 | + | 0.193967i | ||||
\(960\) | 2046.67 | + | 3544.94i | 0.0688084 | + | 0.119180i | ||||
\(961\) | −28766.2 | −0.965601 | ||||||||
\(962\) | 1835.45 | + | 1263.37i | 0.0615147 | + | 0.0423418i | ||||
\(963\) | −60.5972 | −0.00202774 | ||||||||
\(964\) | 13728.1 | + | 23777.7i | 0.458663 | + | 0.794428i | ||||
\(965\) | 12226.6 | + | 21177.2i | 0.407865 | + | 0.706443i | ||||
\(966\) | −8605.32 | + | 14904.9i | −0.286617 | + | 0.496435i | ||||
\(967\) | −42110.1 | −1.40038 | −0.700191 | − | 0.713956i | \(-0.746902\pi\) | ||||
−0.700191 | + | 0.713956i | \(0.746902\pi\) | |||||||
\(968\) | −8843.65 | + | 15317.7i | −0.293642 | + | 0.508604i | ||||
\(969\) | −8708.83 | + | 15084.1i | −0.288718 | + | 0.500074i | ||||
\(970\) | −3093.47 | −0.102397 | ||||||||
\(971\) | 6913.86 | − | 11975.2i | 0.228503 | − | 0.395779i | −0.728862 | − | 0.684661i | \(-0.759950\pi\) |
0.957365 | + | 0.288882i | \(0.0932836\pi\) | |||||||
\(972\) | −710.841 | − | 1231.21i | −0.0234570 | − | 0.0406288i | ||||
\(973\) | 11633.7 | + | 20150.2i | 0.383309 | + | 0.663911i | ||||
\(974\) | 13262.3 | 0.436295 | ||||||||
\(975\) | −3550.69 | + | 1690.52i | −0.116629 | + | 0.0555281i | ||||
\(976\) | −1676.38 | −0.0549791 | ||||||||
\(977\) | −566.943 | − | 981.973i | −0.0185651 | − | 0.0321557i | 0.856594 | − | 0.515992i | \(-0.172576\pi\) |
−0.875159 | + | 0.483836i | \(0.839243\pi\) | |||||||
\(978\) | −1341.90 | − | 2324.23i | −0.0438743 | − | 0.0759926i | ||||
\(979\) | −3986.65 | + | 6905.09i | −0.130147 | + | 0.225421i | ||||
\(980\) | −31891.9 | −1.03954 | ||||||||
\(981\) | 2440.90 | − | 4227.76i | 0.0794413 | − | 0.137596i | ||||
\(982\) | 10558.4 | − | 18287.6i | 0.343107 | − | 0.594279i | ||||
\(983\) | 26250.2 | 0.851729 | 0.425865 | − | 0.904787i | \(-0.359970\pi\) | ||||
0.425865 | + | 0.904787i | \(0.359970\pi\) | |||||||
\(984\) | −7365.87 | + | 12758.1i | −0.238633 | + | 0.413325i | ||||
\(985\) | −6206.98 | − | 10750.8i | −0.200783 | − | 0.347766i | ||||
\(986\) | 6896.84 | + | 11945.7i | 0.222759 | + | 0.385829i | ||||
\(987\) | −48413.7 | −1.56132 | ||||||||
\(988\) | 29786.0 | − | 14181.4i | 0.959128 | − | 0.456651i | ||||
\(989\) | 12600.3 | 0.405124 | ||||||||
\(990\) | 3049.64 | + | 5282.13i | 0.0979028 | + | 0.169573i | ||||
\(991\) | 14680.2 | + | 25426.8i | 0.470566 | + | 0.815045i | 0.999433 | − | 0.0336599i | \(-0.0107163\pi\) |
−0.528867 | + | 0.848705i | \(0.677383\pi\) | |||||||
\(992\) | −2999.92 | + | 5196.01i | −0.0960156 | + | 0.166304i | ||||
\(993\) | −22957.7 | −0.733676 | ||||||||
\(994\) | 7572.87 | − | 13116.6i | 0.241647 | − | 0.418544i | ||||
\(995\) | 27192.3 | − | 47098.4i | 0.866384 | − | 1.50062i | ||||
\(996\) | 5931.86 | 0.188713 | ||||||||
\(997\) | −8417.95 | + | 14580.3i | −0.267401 | + | 0.463153i | −0.968190 | − | 0.250216i | \(-0.919498\pi\) |
0.700789 | + | 0.713369i | \(0.252832\pi\) | |||||||
\(998\) | −6831.85 | − | 11833.1i | −0.216692 | − | 0.375321i | ||||
\(999\) | −437.737 | − | 758.182i | −0.0138632 | − | 0.0240118i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 39.4.e.c.16.3 | ✓ | 8 | |
3.2 | odd | 2 | 117.4.g.e.55.2 | 8 | |||
4.3 | odd | 2 | 624.4.q.i.289.4 | 8 | |||
13.2 | odd | 12 | 507.4.b.h.337.5 | 8 | |||
13.3 | even | 3 | 507.4.a.m.1.2 | 4 | |||
13.9 | even | 3 | inner | 39.4.e.c.22.3 | yes | 8 | |
13.10 | even | 6 | 507.4.a.i.1.3 | 4 | |||
13.11 | odd | 12 | 507.4.b.h.337.4 | 8 | |||
39.23 | odd | 6 | 1521.4.a.bb.1.2 | 4 | |||
39.29 | odd | 6 | 1521.4.a.v.1.3 | 4 | |||
39.35 | odd | 6 | 117.4.g.e.100.2 | 8 | |||
52.35 | odd | 6 | 624.4.q.i.529.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
39.4.e.c.22.3 | yes | 8 | 13.9 | even | 3 | inner | |
117.4.g.e.55.2 | 8 | 3.2 | odd | 2 | |||
117.4.g.e.100.2 | 8 | 39.35 | odd | 6 | |||
507.4.a.i.1.3 | 4 | 13.10 | even | 6 | |||
507.4.a.m.1.2 | 4 | 13.3 | even | 3 | |||
507.4.b.h.337.4 | 8 | 13.11 | odd | 12 | |||
507.4.b.h.337.5 | 8 | 13.2 | odd | 12 | |||
624.4.q.i.289.4 | 8 | 4.3 | odd | 2 | |||
624.4.q.i.529.4 | 8 | 52.35 | odd | 6 | |||
1521.4.a.v.1.3 | 4 | 39.29 | odd | 6 | |||
1521.4.a.bb.1.2 | 4 | 39.23 | odd | 6 |